Simulation parameter determination method

ABSTRACT

Provided is a method for reduction of calculation amount required for parameter determination, and for reduction of calculation amount required for parameter determination satisfying desired accuracy. It is a method for preferentially selecting analysis objects, which are capable of providing parameter determination in high degree of certainty, and for controlling calculation order of the selected analysis objects using a calculation order list.

INCORPORATION BY REFERENCE

The present application claims priority from Japanese applicationJP2006-149108 filed on May 30, 2006, the content of which is herebyincorporated by reference into this application.

BACKGROUND OF THE INVENTION

This invention relates to a simulation parameter determination method,in particular, relates to the parameter determination method necessaryfor prediction of experimental value by simulation calculation.

With recent progress of a computer, computer simulation has increasinglybeen utilized in many opportunities, in science field. Simulation ofmolecular level chemical reactions occurring in the body is one examplethereof; in particular, simulation of binding reactions between proteinsand low molecular weight compounds is expected in application to drugdiscovery. Because water occupies about 60% of composition, in bindingreactions of molecules in the body, not only molecules directlyparticipating in binding but also a water solvent present around themolecules largely contribute to binding energy. Therefore, highlyprecise calculation of binding energy in a water solvent is required forcomputer simulation. In the case where computer simulation is utilizedin drug discovery, such calculation accuracy is desired that energyerror of calculated value relative to experimental value is within 1.4kcal/mol. This value corresponds to 10 times error in binding constantobtained as experimental measurement result of binding between proteinsand low molecular weight compounds.

In highly precise calculation of solvation energy, defined as energydifference before and after introduction of effect of water, use of acalculation model with high theoretical exactitude is necessary.Explanation will be given on a polarizable continuum model based on thefirst principle quantum chemistry calculation, which is one of such amodel, and parameters introduced therein, with reference to FIG. 1. Thismodel explicitly deals with atomic nucleus and electrons of thecalculation object molecule 101, however, the water solvent 102 is dealtwith as dielectrics including the calculation object molecule 101. Inaddition, as shown by an outline zone in the drawing, definition of aboundary surface 104 between the space 103 occupied by a molecule andother region, namely the space occupied by dielectrics, is required. Theboundary surface can be defined as the surface formed by overlap of thesphere 105 arranged on all atoms constituting the molecule.Approximately, no arrangement of a sphere on a hydrogen atom may beselected. Solvation energy is calculated based on charge present on theboundary surface, as a result of interaction between a molecule and awater solvent. Therefore, definition of the boundary surface has directinfluence on accuracy in calculation. Accordingly, considering theradius 106 of a sphere arranged on an atom, as a parameter specifyingthe boundary surface between a solute and a solvent, determination ofthis value is capable of providing highly accurate calculation ofsolvation energy. Hereafter, this radius is referred to as “an atomicparameter”.

As one of the atomic parameter determination method, there is a methodfor using a gradient matrix. Explanation will be given below on theatomic parameter determination procedure using a gradient matrix, withreference to FIG. 2 and FIG. 3.

FIG. 2 is a flowchart of the atomic parameter determination method usinga gradient matrix. First of all, the energy convergence threshold T2011, the experimental value 2012 of three-dimensional coordinateinformation and salvation energy of a molecule, and the atomic type2013, which is a classification based on chemical similarity of eachatom constituting the molecule, are input from the input apparatus 201.Subsequently, in the atomic parameter initialization step 202, values ofatomic parameters set by each of atomic types are initialized. Then, inthe matrix generation step 203, a matrix that stores salvation energiesof all molecules and salvation energy gradient of all molecules tochange in each atomic parameter, is generated. Next, in thematrix-equation solving step 204, update value vector x is solved, so asto minimize the objective function (expression 1), where A represents amatrix generated; x represents update value vector of atomic parameter;and b represents experimental value vector of solvation energy.g=Σ|Ax−b| ²   (Expression 1)Next, in the atomic parameters update step 205, atomic parameter valueis updated based on the update value vector. Next, in the atomicparameter calculation termination judging step 206, whether the theamount of change in residual sum of squares of solvation energy is belowτ or not, is judged. In the case where the the amount of change is equalto or larger than τ, the matrix generation step 203, the matrix-equationsolving step 204 and the atomic parameters update step 205 are repeated.In the case where the the amount of change of the atomic parameter isbelow τ, the converged atomic parameter value 2071 is output by theoutput apparatus 207.

FIG. 3 is details of processes in the matrix-generating step, thematrix-equation solving step and the atomic parameters update step, inthe atomic parameter determination method using a gradient matrix. Theprocess 302 to be executed in the matrix generation step 301 iscalculation of solvation energies 3021 of all molecules, and solvationenergy gradient 3022 of all analysis objects to change in each atomicparameter. The calculation results are stored in the matrix 3023. Theamount of calculation required for each one of the matrix element 3024shown by open circle marks in the matrix corresponds toone-time-evaluation of salvation energy using the polarizable continuummodel. The process 304 to be executed in the matrix-equation solvingstep 303 is the minimization calculation of objective function g, whichcan be defined by a matrix-equation composed of the matrix 3041, inwhich the number of line generated in the matrix generation step 301 isthe number of molecule, and the number of column is (the number ofatomic type +1); the solution vector 3042 having the number of elementof (the number of atomic type +1); and salvation energy experimentalvalue vector 3043 having the same element number as the number ofmolecule. The matrix 3041 and the salvation energy experimental valuevector 3043 are known, and the solution vector 3042 is unknown amount asan object to be solved. The process 306 to be executed in the atomicparameters update step 305 is to update the new atomic parameter vector3061 by summing the atomic parameter vector 3062 before update and thevector 3063 deleted only top element from the solution vector obtainedin the matrix equation solving step 303. Each of the elements of thevector 3063 represents the amount of change in atomic parameter value inthe next loop. Because updating of the atomic parameter results inchange in salvation energy or solvation energy gradient to change inatomic parameter, calculations are repeated from the matrix generationstep to the atomic parameters update step until g<τ is satisfied.

Such the atomic parameter determination method has two problems.

The first problem is vast amounts of calculation required for thecalculation 3021 of solvation energies of all molecules and thecalculation 3022 of salvation energy gradient of all molecules relativeto change in each atomic parameter, in the matrix generation step 301.It is because, in the first principle quantum chemistry calculation,molecular integration is calculated, which increases the amount ofcalculation in the order of m power of atomic number (m=3, 4, 5, . . . ,depending on calculation methods), to express inter-electroninteractions. When the amount of calculation required for calculation ofsalvation energy in one time is 1, the amount of calculation requiredfor calculation of salvation energy gradient in one time in a finitedifference method is also 1; therefore, total amount of calculationrequired for matrix generation equals to the number of the matrixelement 3024 shown by open circle marks in the matrix 3023. Because thematrix generation step is repeated until convergence of solvationenergy, total amount of calculation required for parameter determinationis (the number of matrix element x the number of iteration).

In more generally, N represents the number of molecules used in atomicparameter determination; A(n) represents the number of atoms included inthe molecule n; f(A(n)) represents the amount of calculation requiredfor salvation energy calculation of the molecule n. As described above,f(A(n)) is a power function of A(n). In addition, p(n) represents thenumber of atomic types included in the molecule n; and T represents theamount of calculation.

In the prior art using a gradient matrix, calculation is repeated untilthe amount of change in atomic parameter is below energy convergencethreshold. When the number of iteration is expressed by I, then theamount of calculation is expressed by (expression 2). $\begin{matrix}\begin{matrix}{T_{conventional} = {I{\sum\limits_{n = 1}^{N}{\left( {1 + {p(n)}} \right){f\left( {A(n)} \right)}}}}} \\{= {\sum\limits_{n = 1}^{N}{\left( {I + {I \cdot {p(n)}}} \right){f\left( {A(n)} \right)}}}}\end{matrix} & \left( {{Expression}\quad 2} \right)\end{matrix}$

The subsequent term after summation symbol at the right-hand side of thefirst line of expression 2 is the amount of calculation required formatrix generation in one time, and “1” in the summation symbolcorresponds to solvation energy calculation, and p(n) corresponds togradient calculation of solvation energy relative to change in atomicparameter value.

Supplementary explanation will be given on the first problem using thespecific examples. FIG. 4 is an application example of the atomicparameter determination method using a gradient matrix to 10 molecules.In this drawing, the atomic type 401, the resultant atomic parametervalue 402, and the atomic type 403, which each molecule contains, areshown. As the atomic type 401, the following 6 kinds were defined:CH₃(C), CH₃(N), CH₂(CC), CH₂(CN), NH₂(C), and NH₂(N). Atom(s) shown inthe parenthesis shows atom(s) of bonding partner. For example, theatomic type CH₂(CN) represents carbon atom of CH₂ having bond with onecarbon atom and one nitrogen atom. The atomic type 403 corresponding toeach molecule was shown by open circle marks. For example, inCH₃—CH₂—NH₂ of the sixth molecule, CH₃ belongs to the CH₃(C) atomictype, because it bonds to CH₂; CH₂ belongs to the CH₂ (CN) atomic type,because it bonds to CH₃ and NH₂; and NH₂ belongs to the NH₂(C) atomictype, because it bonds to CH₂. As a result, open circle marks areprovided at three sites in this molecule. As an exception in the presentatomic parameter determination method, for the non-methyl carbon atom of(CH₃)₄—C of the ninth molecule, a fixed value of 1.7 was used; becausethis atom is surrounded by 4 methyl groups and thus it is difficult tocontact with water molecules and is thought that contribution tosalvation energy is small.

As for initial values of atomic parameters, 1.7 was used for 4 kinds ofCH₃(C), CH₃(N), CH₂(CC) and CH₂ (CN), and 1.4 for 2 kinds of NH₂(C) andNH₂(N). As a specific method for solving, a solution vector wasapproximately determined every iteration time, by a steepest gradientmethod to be described below, to update atomic parameter. In addition,to accelerate atomic parameter convergence, atomic parameter was updatedusing the solution of past iterations, once four iterations. Detailswill be given below.

-   1) An update method every iteration-   1-1) As for each atom “a” not equivalent in view of symmetry, which    composes each molecule n, Taylor expansion of solvation energy En is    terminated at the first order term, and based on the resultant    equation and energy residue Z_(n), atomic parameter, r_(n,a,t), and    weight thereof, W_(n,a,t), are calculated; (Expression 3) and    (Expression 4). $\begin{matrix}    {r_{n,a,t} = {r_{n,a,{t{({old})}}} - \frac{z_{n}}{\frac{\partial E_{n}}{\partial r_{n,a,}} \cdot w_{n,a,t}}}} & \left( {{Expression}\quad 3} \right) \\    {w_{n,a,t} = \frac{\left( \frac{\partial E_{n}}{\partial r_{n,a,t}} \right)^{2}}{\sum\limits_{t}\left( \frac{\partial E_{n}}{\partial r_{n,a,t}} \right)^{2}}} & \left( {{Expression}\quad 4} \right)    \end{matrix}$-   1-2) Updated value r_(t) of the atomic parameter is calculated as    weighted average of r_(n,a,t), obtained for each molecule n.    $\begin{matrix}    {r_{t} = \frac{\sum\limits_{n,a}{r_{n,a,t} \cdot w_{n,a,t}}}{\sum\limits_{n,a}w_{n,a,t}}} & \left( {{Expression}\quad 5} \right)    \end{matrix}$-   2) An update method every four iterations-   2-1) As for each atom “a” composing each molecule n and not    equivalent in view of symmetry, a straight line z_(n)=A r_(n,a,t)+B,    which approximates hysteresis of the atomic parameters r_(n,a,t(I)),    and residue z_(n,(I)) at I=4i−3, 4i−2, 4i−1, and 4i, is determined    to calculate the atomic parameter value in which the residue becomes    0, as r_(n,a,t)=−B/A, assuming that I is the number of iteration;    and I is an integer.-   2-2) As for each atomic type t, updated value r_(t) of the atomic    parameter is calculated as average of the resultant r_(n,a,t). Sum    on delta function of the denominator is the number of atoms    belonging to atomic type t, among atoms composing molecule n and not    equivalent in view of symmetry. (Expression 6) $\begin{matrix}    {r_{t} = \frac{\sum\limits_{n,a}r_{n,a,t}}{\sum\limits_{n,a}\delta_{t_{n,a},t}}} & \left( {{Expression}\quad 6} \right)    \end{matrix}$

FIG. 5 shows the amount of calculation and calculation error obtained bythe application of the atomic parameter determination method using theabove-explained gradient matrix. In this drawing, the abscissa axis isthe amount of calculation, which was defined as the calculation time 501required for atomic parameter determination using one computer, and thelongitudinal axis is the calculation error 502, which was defined asaverage value of absolute calculation errors of each of the molecules.The plot 503 of lozenge marks shows relation between the amount ofcalculation and calculation error. Because this method repeats solvingof a matrix-equation, the calculation error becomes smaller withincrease in the number of iteration. To attain a calculation error of0.1 kcal/mol, the amount of calculation of about 500 minutes isrequired. As shown in this example, the amount of calculation requiredis vast, even in atomic parameter determination using relatively smallnumber of molecules.

The second problem is that calculation accuracy is unpredictable inadvance, when the resultant atomic parameter is applied to predictsalvation energy. In general, calculation accuracy is considered todepend on definition of an atomic type. Therefore, in the case where thecalculation accuracy is below desired accuracy, re-definition of theatomic type, and re-execution of whole procedures of atomic parameterdetermination are required. In this case, iteration of atomic parameterdetermination procedure itself is required, which further expands theamount of calculation.

This atomic parameter determination method can be generalized with thefollowing substitutions: molecules with “analysis objects”; atomscomposing molecules with “elements composing analysis objects”; atomicparameter with “elemental parameter”; experimental values of solvationenergy simply with “experimental values”; and calculated values ofsolvation energy simply with “calculated values”.

FIG. 6 is a flowchart of the parameter determination method using agradient matrix. First of all, the convergence threshold τ 6011, thenecessary information and experimental value 6012 for calculation ofanalysis object, and the elemental type 6013 for each element composingan analysis object are input by the input apparatus 601. Subsequently,in the elemental parameter initialization step 602, elemental parameterset by each of elemental types is initialized. Then, in the matrixgeneration step 603, a matrix, which stores the calculated value of allanalysis objects, and the gradient of calculated value of all analysisobjects relative to change in each elemental parameter is generated.Then in the matrix-equation solving step 604, such an updated valuevector x, that minimizes the objective function g=Σ|Ax−b|², is solved,assuming that A represents a matrix generated; x represents updatedvalue vector of elemental parameter; and b represents experimental valuevector. Next, in the elemental parameters update step 605, value ofelemental parameter is updated based on update value vector. Next, inthe elemental parameter calculation termination judging step 606,whether the amount of change in residual sum of squares is below τ ornot, is judged. In the case where the amount of change is equal to orlarger than τ, the matrix generation step 603, the matrix-equationsolving step 604 and the elemental parameters update step 605 arerepeated. In the case where the amount of change of the elementalparameter is below τ, the converged elemental parameter 6071 is outputby the output apparatus 607.

FIG. 7 is the details of processes in the matrix generation step,matrix-equation solving step and elemental parameters update step in theparameter determination method using a gradient matrix. The process 702to be executed in the matrix generation step 701 is calculation of thecalculated value 7021 of all analysis objects, and the gradients 7022 ofcalculated value of all analysis objects relative to change in eachelemental parameter. The calculation results are stored in the matrix7023. The amount of calculation required for each of the matrix elements7024, shown by open circle marks in the matrix, corresponds to one-timeevaluation of calculated value. The process 704 to be executed in thematrix-equation solving step 703 is the calculation to minimize theobjective function g, which can be defined by a matrix-equation composedof the matrix 7041 composed of analysis object number as the number ofline, and (elemental type number +1) as the number of column, generatedin the matrix generation step 701, and the solution vector 7042 havingthe number of element of (elemental type number +1) and the experimentalvalue vector 7043 having the same elemental number as analysis objectnumber. The matrix 7041 and the experimental value vector 7043 areknown, and the solution vector 7042 is unknown amount as an object to besolved. A plurality of solving methods are present for thematrix-equation, however, it is premised on that rate determining stepof calculation is the matrix generation step and not the matrix-equationsolving step, therefore, a specific method for solving may be arbitraryhere. The process 706 to be executed in the elemental parameters updatestep 705 is to update the new elemental parameter vector 7061 by sum ofthe elemental parameter vector 7062 before update and the vector 7063deleted only top element from the solution vector obtained in thematrix-equation solving step 703. Each element of the vectors 7063represents the amount of change in the next loop of value of elementalparameter. When the elemental parameter is updated, calculation value orgradient of calculation value relative to elemental parameter willchange, therefore, calculations are repeated again from the matrixgeneration step.

In the generalized parameter determination method, in the case wherematrix element calculation occupies a large portion in totalcalculation, it raises a problem that the amount of calculation requiredfor repeated solving of the matrix-equation becomes vast. The amount ofcalculation is given by expression 2. However, function form of f(A(n))differs depending on analysis objects. In addition, in the case whereparameter determination result does not satisfy desired accuracy,re-definition of the parameter and iteration of the parameterdetermination procedure itself are required, which further expands theamount of calculation required.

To solve the above first problem, it is an object of this invention toreduce the amount of calculation required for parameter determination.

In addition, it is a second object of this invention to reduce theamount of calculation required for parameter determination satisfyingdesired accuracy, to solve the above second problem.

SUMMARY OF THE INVENTION

To solve the above first problem, in the parameter determination methodrelevant to the embodiment of this invention, only molecules having thenumber of undetermined atomic parameter of equal to or less than 1 areselected, and thus selected molecules are stored in a calculation ordercontrol list; and based on this list, the undetermined atomic parametersare sequentially determined. Selection of molecules is repeated untilall atomic parameters are determined.

At the first round of atomic parameter determination procedure byiteration, a molecule having the number of undetermined atomic parameterof 1 is selected. In order to reproduce, by calculation, experimentalvalue of salvation energy of such a molecule, determination of only oneatomic parameter value is needed. Therefore, atomic parameter canunambiguously be determined.

Then, a molecule having the number of undetermined atomic parameters of2 is considered. When one of the two undetermined atomic parameters canbe tentatively determined based on atomic parameter value determined inthe first round of iteration, then the number of undetermined atomicparameter becomes 1, and determination of only this one atomic parameteris left. In the case where reliability of the tentatively determinedatomic parameter is high, newly determined atomic parameter is alsodetermined with high degree of certainty.

In order to determine tentatively atomic parameter in high reliability,atomic charge and averaged bond distance are calculated in advance oneach of the atoms. Then, the atomic parameter is expressed as a functionwith atomic charge and averaged bond distance as variables. Atomiccharge is quantity relating to Coulomb interaction strength betweenmolecule and water solvent, and averaged bond distance is quantityreflecting bond environment such as the number of bonded atoms of amolecule, bond order, atoms of bonding partner and the like. Therefore,atoms having similar atomic charge and averaged bond distance areconsidered to be similar also in values of atomic parameters.

However, atomic parameter obtained by the above method has no guaranteeto be capable of giving determination of salvation energy in desiredaccuracy, for example, 1.4 kcal/mol. Therefore, to solve the abovesecond problem, in the parameter determination method relevant to theembodiment this invention, first of all, acceptable energy error is set,which is defined as maximal acceptable value of difference betweencalculated value of solvation energy obtained by simulation calculation,and experimental value of solvation energy. Then, whether absolute valueof calculation error, defined by difference between calculated value andexperimental value, is within acceptable error or not, is judged on eachof the molecules, in sequential determination process of undeterminedatomic parameter based on the calculation order control list.

In the case where absolute value of calculation error is larger thanacceptable error, one atomic parameter, which gives largest contributionto salvation energy, is noticed among a plurality of atomic parameterscontained in a molecule, so as to make calculated value closer toexperimental value. This atomic parameter value, although tentativelydetermined, is re-set to be undermined, to determine newly atomicparameter value. In this method, acceptable error is fixed instead ofthe number of atomic parameter.

It was explained above that atomic parameter value was expressed as afunction with atomic charge and averaged bond distance as variables. Asshown in the above example, in the case where tentatively determinedatomic parameter based on a simple function is re-set newly as beingundermined to execute re-determination process, the function thatexpresses atomic parameter value becomes more complicated.

An example will be given on the case where 2 atomic parameters arealready determined on a certain atomic type, and values of the atomicparameters are expressed with a linear function of atomic charge as avariable. Atomic parameter value of other atom belonging to the sameatomic type can be tentatively determined by substitution of atomiccharge of the atom into the linear function expressing atomic parametervalue. In the case where the tentatively determined atomic parametervalue was re-set as being undermined in a process of atomic parameterdetermination, and the value was re-determined, value of the atomicparameter of three atoms belonging to the noticed atomic type cannot beexpressed by a linear function with atomic charge as a variable.However, the atomic parameter value can be expressed by using a linearfunction with both atomic charge and averaged bond distance asvariables, or more complicated functions like two kinds of linearfunctions with atomic charge as a variable. Therefore, in thisinvention, a function expressing value of each of atomic parameters ismade complicated in atomic parameter determination process, so thatabsolute value of calculation error is within acceptable error.

Explanation was given above on the atomic parameter determination methodused for calculation of salvation energy of a molecule, as an example.In generalization of this example to analysis objects such as materials,parts, structures and the like instead of molecules, a means forcontrolling of calculation order of analysis objects using calculationorder list is considered to be effective. Applicable scope of thisinvention is the case where a calculation object can be divided toelement and attribute value can be defined to each element, and also thecase where evaluation of calculated value or gradient relative toparameter change of calculated value is a rate-determining step. Inaddition, such a means is also considered effective that value ofelemental parameter is expressed by a function of value of elementalproperty, and, if necessary, a function form is made complicated, sothat difference between experimental value such as characteristic valueor property measured on a calculation object, and calculated valueobtained by simulation is within acceptable error. The applicable scopeof this means is the case where increase in the number of parameter isallowed, which is used to fit experimental value and calculated value.

A means for selection of only a molecule having the number ofundetermined atomic parameter equal to or less than 1, has effect todetermine preferentially atomic parameter which can be determined withhigh degree of certainty. For example, a benzene molecule is composed of6 carbon atoms, and they are equivalent in view of symmetry, thereforethe number of atomic parameter can be said to be 1. Therefore, atomicparameter value, which reproduces experimental value of salvation energyof benzene, is determination with high degree of certainty, and in thiscase, unambiguously.

In addition, a means for storing the calculation order control list, andfor iteration of one-variable equation solving based on the list tosequentially determine undermined atomic parameter does not require thematrix generation step as in a conventional technique. Therefore, thismethod has effect of reducing the amount of calculation required foratomic parameter determination. In a conventional technique, calculationwas iterated on solvation energy of all molecules and salvation energygradient of all molecules relative to change in each of the atomicparameters. On the other hand, embodiments of this invention determinecalculation order of molecules, and calculation is iterated on salvationenergy of each of the molecules and salvation energy gradient relativeto change in one atomic parameter.

In addition, a means for re-setting the tentatively determined atomicparameter value on a certain molecule, as being undermined, to determinenewly atomic parameter value, in a process of sequential determinationof undetermined atomic parameter by iteration of solving of aone-variable equation, based on the calculation order control list, haseffect of reproducing solvation energy in desired accuracy. It isbecause new re-determination of the tentatively determined atomicparameter value is capable of improving calculation accuracy ofsalvation energy. Under the condition that increase in the number ofparameter used to reproduce experimental value of salvation energy isacceptable, re-definition of atomic type and re-execution of wholeprocedure of atomic parameter determination can be avoided using thismeans.

The above effect is similarly obtained also in the case of consideringanalysis objects such as materials, parts, structures and the likeinstead of molecules. A means for selecting only one molecule having thenumber of undetermined atomic parameter equal to or less than 1, haseffect to determine preferentially elemental parameter that can bedetermined in high degree of certainty. In addition, a means for storingthe selected analysis object into the calculation order control list,and for iteration of one-variable equation solving based on the list tosequentially determine undermined elemental parameter does not requirethe matrix generation step as in a conventional technique. Furthermore,a means for re-setting the tentatively determined elemental parametervalue on a certain analysis object, as being undetermined, to determinenewly elemental parameter value, in a process of sequentialdetermination of undetermined elemental parameter by iteration ofsolving of a one-variable equation, based on the calculation ordercontrol list, has effect to reproduce calculated value in desiredaccuracy.

According to this invention, the amount of calculation can be reduced ascompared with the prior art.

Other objects, features and advantages of the invention will becomeapparent from the following description of the embodiments of theinvention taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a polarizable continuum model and parameters used in themodel.

FIG. 2 is a flowchart of the atomic parameters determination methodusing a gradient matrix.

FIG. 3 shows details of processes in the matrix generating step,matrix-equation solving step, and atomic parameters update step in theatomic parameter determination method using a gradient matrix.

FIG. 4 shows an atomic type definition, determined parameters values,and atomic types corresponding to each molecule in the atomic parameterdetermination method using a gradient matrix.

FIG. 5 shows an amount of calculation and calculation error in theatomic parameter determination method using a gradient matrix.

FIG. 6 is a flowchart of the parameters determination method using agradient matrix.

FIG. 7 shows details of processes in the matrix generation step,matrix-equation solving step, and elemental parameters update step inthe parameter determination method using a gradient matrix.

FIG. 8 is a flowchart of the atomic parameters determination method.

FIG. 9 shows details of processes in calculation order list generationstep, the one-variable equation solving step, and the atomic parametersupdate step in the atomic parameter determination method.

FIG. 10 shows an input of molecular information.

FIG. 11 shows an input of atomic information.

FIG. 12 shows an initialization of atomic parameters.

FIG. 13 shows a hardware control approach in the one-variable equationsolving step.

FIG. 14 shows an example of atomic parameters update in the case thatvalue of atomic parameter is expressed by a linear function of a valueof an atomic attribute.

FIG. 15 shows an example of atomic parameters update in the case thatvalue of atomic parameter is expressed by a linear function of values oftwo atomic attributes.

FIG. 16A shows an atomic type definition used in the application of thisinvention, process of atomic parameter values determination, and atomictype corresponding to each molecule.

FIG. 16B shows an atomic type definition used in the application of thisinvention, process of atomic parameter values determination, and atomictype corresponding to each molecule.

FIG. 16C shows an atomic type definition used in the application of thisinvention, process of atomic parameter values determination, and atomictype corresponding to each molecule.

FIG. 16D shows an atomic type definition used in the application of thisinvention, process of atomic parameter values determination, and atomictype corresponding to each molecule.

FIG. 17 shows a comparison of amount of calculation and calculationerror between this invention and the prior art.

FIG. 18 shows a comparison of solvation energy prediction accuracy.

FIG. 19 is a flowchart of the parameter determination method.

FIG. 20 shows details of processes in calculation order list generationstep, one-variable equation solving step, and elemental parametersupdate step in the parameter determination method.

FIG. 21 is a flowchart of the atomic parameter determination methodunder the fixed acceptable error condition.

FIG. 22 shows details of processes in calculation order list generationstep, one-variable equation solving step, and atomic parameters updatestep, in the atomic parameter determination method under the fixedacceptable error condition.

FIG. 23 shows details of calculation order list update step.

FIG. 24A shows an example of atomic parameter update in the case thatvalue of atomic parameter is expressed by a linear function of value ofan atomic attribute.

FIG. 24B shows an example of atomic parameter update in the case thatvalue of atomic parameter is expressed by a linear function of value ofan atomic attribute.

FIG. 25A shows an example of atomic parameters update in the case thatvalue of atomic parameter is expressed by a linear function of values oftwo atomic attributes.

FIG. 25B shows an example of atomic parameters update in the case thatvalue of atomic parameter is expressed by a linear function of values oftwo atomic attributes.

FIG. 26 shows a comparison of the amount of calculation when the numberof molecules N used in the atomic parameter determination issufficiently large.

FIG. 27 shows a comparison of the amount of calculation between theprior art and this invention in the atomic parameter determinationmethod using 63 molecules.

FIG. 28 is a flowchart of simulation parameter determination methodunder the fixed acceptable error condition.

FIG. 29 shows details of processes in calculation order list generationstep, the one-variable equation solving step, and the elementalparameters update step, in the parameter determination method under thefixed acceptable error condition.

FIG. 30 is a flowchart of atomic parameter determination methodincluding information display step.

FIG. 31 shows an example of screen display in calculation order listdisplay step.

FIG. 32 shows an example of screen display in the calculation progressdisplay step.

FIG. 33 shows an example of data view at the atomic parameters displaystep.

DESCRIPTION OF THE INVENTION

Explanation will be given below on embodiments of this invention withreference to drawings.

Embodiment 1

Explanation will be given on the atomic parameter determination methodof this invention, with reference to FIG. 8 and FIG. 9.

FIG. 8 is a flowchart of the atomic parameter determination method.First of all, the energy convergence threshold τ 8011, thethree-dimensional coordinate information determined by calculation orexperiment, and experimental value 8012 of solvation energy for amolecule, atomic type of each atom composing a molecule, and the atomictype, atomic charge, and averaged bond distance 8013 for each atom areinput by the input apparatus 801. Subsequently, in the initializationstep 802, the atomic parameter initialization step 8021 set by each ofatomic types and the sorting up step 8022 of all molecules by the numberof undetermined atomic parameters are executed. Then, in calculationorder list generation step 803, the selection step 8031 of a molecule,having the number of undetermined atomic parameters is 1, from amolecule containing undetermined atomic parameter and the calculationorder list generation step 8032, which stores sorting up result ofselected molecules by number of atomic parameters, are executed. Then inthe one-variable equation solving step 804, solving of a one-valuableequation is iterated on a molecule on the top of calculation order list,until the amount of change of calculated value of salvation energybecomes below τ, and the undetermined atomic parameter determinationstep 8041 and calculation order list update step 8042 are executed. Incalculation order list termination judging step 8043, in the case wherea molecule is still present on the top of calculation order list,procedure is returned to the step 8041; in the case where such amolecule is not present any more, procedure is forwarded to the atomicparameters update step 805.

Next, in the atomic parameters update step 805, on an atomic typecorresponding to determined atomic parameter, the atomic parameterexpression formula update step 8051, which equation being a function ofatomic charge and averaged bond distance, the sorting up step 8052 ofundetermined molecules by the number of undetermined atomic parameters,the sorting down step 8053 of molecules with the identical number ofundetermined atomic parameters by the number of atomic parameters, andthe undetermined molecule update step 8054 are executed. In the atomicparameter calculation termination judging step 806, whether anundetermined molecule is present or not, is judged. In the case wherethe undetermined molecule is present, calculation order list generationstep 803, the one-variable equation solving step 804 and the atomicparameters update step 805 are iterated. In the case where theundetermined molecule is not present, calculation error of each moleculeis calculated using the resultant atomic parameter, in the calculationerror computing step 807, and the determined atomic parameter value 8081is output by the output apparatus 808.

FIG. 9 is details of processes in calculation order list generationstep, the one-variable equation solving step, and the atomic parametersupdate step in the atomic parameter determination method. As an example,explanation will be given on the first and the second rounds ofiterations of each of the steps, in the case of the number of moleculesof 9, and the number of atomic types of 8. In the first round process902 to be executed in calculation order list generation step 901, themolecule having the number of undetermined atomic parameter of 1, themolecule 9022 (molecule 8, molecule 3 and molecule 4) having the numberof undetermined atomic parameter of 1, are selected from moleculessorted up by the number 9021 of undetermined atomic parameters inadvance. Calculation order of these molecules is molecule 8, molecule 3and molecule 4, namely the same as the arrangement order of themolecules, and this order is stored in calculation order list 9023. Inthe first round process 904 to be executed in the one-variable equationsolving step 903, undetermined atomic parameter is determined based oncalculation order list. Because the first calculation is on molecule 8,salvation energy is calculated first, using atomic parameter r_(a,8),and value of r_(a,8) is adjusted so as to reproduce experimental valueE8. In this process, value that can reproduce experimental value issearched while changing r_(a,8), therefore, iterated solving of aone-variable equation is required. Similar process is executed on thetwo selected molecules left. In the first round process 906 to beexecuted in the atomic parameters update step 905, expression formula ofatomic parameter as a function of atomic charge and averaged bonddistance, is updated on a, b and h that are the atomic type 9061corresponding to determined atomic parameter. Expression formula ofatomic parameter may be a function of either one of atomic charge oraveraged bond distance. For example, the atomic parameter 9062 of anatomic type a can be expressed as r_(a)(q)=c₀+c₁q; where c₀ and c₁ arecoefficients. Then, undetermined atomic parameter value classified toatomic type “a” is obtained by substitution of atomic charge q intor_(a)(q)=c₀+c₁q. However, on the atom 9063, which atomic charge is apartthat of other atom belonging to the same atomic type by certainthreshold or more from, there may be an option of not setting atomicparameter value. The “value assigned” atom 910 is shown by a filledcircle, and the value not assigned, namely the “value not assigned”(undetermined) atom 911 is shown by an open circle. Then, at this time,6 molecules, namely molecules 5, 6, 7, 2, 1 and 9, are sorted up by thenumber 9064 of undetermined atomic parameters. In addition, in the casewhere number of undetermined parameters is the same, the molecules arearranged in sort down of the number 9065 of atomic parameters. Here,molecules having the number of undetermined parameters of equal to orlarger than 1 become new undetermined molecules. Molecule 2 has thenumber of undetermined parameters of 0 at this moment, thus is not usedin atomic parameter determination. In the second round process 907 to beexecuted in calculation order list generation step 901, the molecule9072 having the number of undetermined atomic parameters 9071 of 1(molecule 5, and molecule 6) are selected from molecules arranged inadvance. Calculation order of these molecules is molecule 5, andmolecule 6, and this order is stored in calculation order list 9073. Inthe second round process 908 to be executed in the one-variable equationsolving step 903, undetermined atomic parameter is determined based oncalculation order list. Solvation energy is calculated first, usingatomic parameter r_(a,5) under fixed value condition, and undeterminedatomic parameter r_(d,5), and value of r_(d,5) are determined so as toreproduce experimental value E₅. In this process, value that canreproduce experimental value is searched while changing only r_(d,5),therefore, process to be executed is iterated solving of a one-variableequation, even for a molecule composed of 2 atomic parameters. Similarprocess is executed on the 2 selected molecules left. In the secondround process 909 to be executed in the atomic parameters update step905, expression formula of atomic parameter, as a function of atomiccharge and averaged bond distance, is updated on a, b, h, d and e thatare the atomic type 9091 corresponding to determined atomic parameter.For example, the atomic parameter 9092 of atomic type “a” is updatedfrom r_(a)(q)=c₀+c₁q to r_(a)(q)=c′₀+c′₁q. After updating expressionformula and determination of atomic parameter value of an atomclassified to the corresponding atomic type, re-arrangement operation ofundetermined molecule is iterated in the same manner as the first roundof iteration. This process is iterated until undetermined molecules areabsent.

Explanation will specifically be given on embodiment of process inrelation to a part of the step of a flowchart of the atomic parameterdetermination method shown by FIG. 8.

An example of the input 8012 of three-dimensional coordinate informationof a molecule and experimental value of salvation energy is shown inFIG. 10. In addition, an example of the input 8013 of an atomic type t,atomic charge q, and averaged bond distance 1 for each atom composing amolecule, is shown in FIG. 11. Because these inputs are mutuallyrelated, explanation will be given on both of FIG. 10 and FIG. 11 at thesame time. First of all, input information can be classified intomolecular information and atomic information. Input informationattributed to molecule includes the three-dimensional coordinateinformation 1001 of a molecule. As an example, the structure 1002 ofpara-xylene molecule was shown. Actual input is three-dimensionalcoordinates of each of the atoms composing the molecule. In addition,input information attributed to molecule includes the experimental value1003 of solvation energy. The experimental value 1004 of solvationenergy of a para-xylene molecule is −0.80 kcal/mol. The number 1005 ofatomic parameter to be determined are 3 kinds, open circle, filledcircle and hatched circle, using the example 1006 of a para-xylenemolecule. Because the atoms with the same kind of mark are equivalent inview of symmetry, they have the same atomic parameter value. Thisinformation is not essential to parameter determination calculation,however, preparation thereof in advance provides convenience. Atomicinformation includes an atomic type 1101, an atomic charge 1102 and anaveraged bond distance 1103. A molecule of para-xylene has 3 kinds ofatomic parameters, and the atomic type, the atomic charge and theaveraged bond distance are input on each thereof. Specifically, theatomic charge was determined by charge assignment algorism on each ofthe atomic nuclei composing the molecule, so as to provide bestapproximation of static potential of the molecule. The averaged bonddistance was calculated as average value of bond distance for the atomto which each of the atoms directly bonds.

FIG. 12 shows an example of initialization 8021 of the atomic parameterr_(t)(q, 1), set by each of the atomic types. It is also convenient hereto classify information to be handled into molecular information andatomic information. The atomic information 1201 includes the value 1202of each atomic parameter and the status 1203 of atomic parameter. Thestatus of atomic parameter is either the “value assigned” 1204 or the“value not assigned” 1205. As initialization value, values are notdefined for all atomic parameters, and thus the status is treated as“value not assigned”. The molecular information 1206 can be calculatedby summation of sets of atomic information. The number 1207 of “valueassigned” atomic parameters contained in a molecule is the number ofatomic parameter where an atomic parameter status is “value assigned”,and the number 1208 of “value not assigned” atomic parameters also cansimilarly be calculated. The calculation status 1209 of a molecule iseither “unfinished” or “finished”; in the case where all of the atomicparameters are “value assigned”, the calculation status 1209 of amolecule thereof becomes “finished”. The initial value 1210 of molecularinformation is only summation result of initial value sets of atomicinformation. In the case of para-xylene, the initial value 1211 ofnumber of “value assigned” atomic parameters contained in a molecule is0, and the number 1212 of “value not assigned” atomic parameters is 3,the same as number of atomic parameters. The initial value 1213 of acalculation status is “unfinished”.

Embodiment of this invention is characterized by having the step thatcontrols calculation order of solvation energy of a molecule usingcalculation order list. Explanation will be given on a hardware controlapproach in the one-variable equation solving step 804, using FIG. 13.

The following process is executed on a molecule listed on the top ofcalculation order list 1301. First of all, in the input file generationstep 1302, the input file 1303 for salvation energy calculation isprepared based on three-dimensional coordinate information of themolecule that was input in advance, and information of “value assigned”atomic parameter. For “value not assigned” atomic parameter, setting ofsuitable value is necessary. For example, van der Waals' radius valuespecified by each element may be used. In the solvation energycalculation job input step 1304, the input file 1303 is delivered to thesalvation energy calculation program 1306 that is installed in thecomputer 1305 to calculate solvation energy. In the calculation resultoutputting step 1307, the calculation result is written in the outputfile 1308 by the salvation energy calculation program 1306. In theoutput result processing step 1309, based on comparison betweenexperimental value of salvation energy of a molecule already input, andcalculated value, atomic parameter is updated. Procedures from the inputfile generation step 1302 to the output result processing step 1309 areiterated until the amount of change of calculation value of solvationenergy becomes below energy convergence threshold. At the termination ofthe iteration, the molecule on the top of calculation order list isdeleted and the next top and lower molecules in the calculation orderare sequentially moved up. The above procedure is continued untilcalculation order list is empty.

Explanation will be given on embodiment of the atomic parameter,r_(t)(q, 1), update step 8051 of atomic type corresponding to determinedatomic parameter, using FIG. 14 and FIG. 15.

FIG. 14 is an example of atomic parameter update in the case that theatomic parameter value 1401 is expressed by a linear function of thevalue 1402 of an atomic attribute such as atomic charge as a variable. Afilled circle in the drawing shows the atom 1403 having “value assigned”atomic parameter, while an open circle shows the atom 1404 having “valuenot assigned” atomic parameter. First of all, the linear function 1405correlating atomic parameter value with value of an atomic attribute isdefined using the “value assigned” atom 1403. Then, the value 1406 of anatomic attribute of a “value not assigned” atom is substituted in alinear function to assign atomic parameter value. Here, value assignedto the “value not assigned” atom 1407 having value of an atomicattribute far apart from value of an atomic attribute of a “valueassigned” atom, may not necessarily be highly precise. Atomic parameterof such a molecule is determined as the last atomic parameter of amolecule to which the atom belongs.

FIG. 15 is an example of atomic parameter update in the case that theatomic parameter value 1501 is expressed by a linear function of twovalues of atomic attribute such as the atomic charge 1502 and theaveraged bond distance 1503 as variables. A filled circle (or a graycircle) in the drawing shows the atom 1504 having “value assigned”atomic parameter, while an open circle shows the atom 1505 having “valuenot assigned” atomic parameter. First of all, the linear function 1506correlating atomic parameter value with value of an atomic attribute isdefined using the “value assigned” atom 1504. Then, the atomic chargeand averaged bond distance 1507 of a “value not assigned” atom issubstituted into a linear function to assign atomic parameter value.Here, value assigned to the “value not assigned” atom having value of anatomic attribute far apart from value of an atomic attribute of a “valueassigned” atom, 1508 may not necessarily be highly precise. Atomicparameter of such a molecule is determined as the last atomic parameterof a molecule to which the atom belongs.

Finally, the amount of calculations obtained by a conventionaldetermination method for atomic parameter, and the atomic parameterdetermination method according to this invention are compared. Theamount of calculation in the prior art is described in expression 2. Inthis invention, molecules are sequentially selected, and calculation isiterated on each of the molecules until the amount of change ofcalculated value of solvation energy becomes below energy convergencethreshold. The number of iteration is represented by I(n), which isdifferent by a molecule. However, there are such molecules as not to beused in atomic parameter calculation. Therefore, the amount ofcalculation can be calculated by “expression 7” using δ function whichis defined 1 for molecules used in atomic parameter determination, and 0for molecules not used. $\begin{matrix}{T_{invention} = {\sum\limits_{n = 1}^{N}{{\delta(n)}\left( {1 + {I(n)}} \right){f\left( {A(n)} \right)}}}} & \left( {{Expression}\quad 7} \right)\end{matrix}$

Comparison between expression 2 and expression 7 shows smaller amount ofcalculation in a method of embodiment of this invention as compared withthe prior art in view of three points. Firstly, calculation is executedon all molecules in the prior. art, while, in embodiment of thisinvention, calculation is executed on a part of the molecules bypresence of the δ function, by which the amount of calculation isreduced. Secondly, the first term in the parenthesis at the right-handside of the second line of expression 2 is “I” in the prior art, whilein embodiment of this invention, the first term in the parenthesis atthe right-hand side of expression 7 is “1”, by which the amount ofcalculation is reduced. Thirdly, the second term in the parenthesis is“I·p(n)” in the prior art, while in Embodiment of this invention, thefirst term in the parenthesis is “I(n)”. The number of iteration, I,required for solving a matrix-equation as a multi-variable non-linearproblem, is considered to be larger than the number of iteration “I(n)”required for solving a one-variable equation as a one-variablenon-linear problem, therefore the amount of calculation in Embodiment ofthis invention is considered less.

Embodiment 2

Explanation will be given on a determination example of 6 atomicparameters using 10 molecules with reference to FIG. 16A to FIG. 18.

FIGS. 16A to 16D show the atomic type 1601 used in the application ofthe present embodiment, the determination process 1602 of atomicparameter value, and the atomic type 1603 corresponding to eachmolecule. As the atomic type 1601, 3 kinds, CH₃, CH₂, and NH₂ weredefined. However, atomic parameters of CH₃, and CH₂, are expressed by alinear function with averaged bond distance 1 as a variable, and atomicparameter of NH₂ is expressed by a linear function with atomic charge qas a variable. Each of the linear functions has 2 variables, therefore,the number of variables to be determined becomes 6. Atomic parametervalue at the initial status is undetermined. Explanation will be givenbelow on determination process of atomic parameter.

First of all, in FIG. 16A, the molecules 1604 (molecules numbered 1, 9,4, 10 and 3) having the number of undetermined atomic parameter of 1,were selected. Atomic parameters to reproduce experimental value ofsalvation energy were determined on each of the molecules selected.

Then, in FIG. 16B, values were assigned for undetermined atomicparameters. As for atomic type CH₃, the atomic parameter r_(CH3) 1605was determined as r_(CH3)=−2.0323*1+4.5674 based on the atomicparameters obtained on molecules numbered 1 and 9. Similarly, the atomicparameter r_(CH3) 1606 was determined as r_(CH2)=3.8382*1−2.9689. As foratomic type NH₂, atomic parameter was still kept “undetermined” at thispoint, because 2 variables necessary in expressing atomic parameter by alinear function were not determined. As for atomic types CH₃ and CH₂,values were assigned to the undetermined atomic parameter 1607 bysubstitution of averaged bond distance 1 to the linear functiondetermined. As a result, the number 1608 of undetermined atomicparameters became 0 as for the molecule 7 and the molecule 5, and 1 asfor the molecule 2, the molecule 6 and the molecule 8.

Then, in FIG. 16C, the molecule 1609 (molecules numbered 2, 6, and 8)having the number of undetermined atomic parameters of 1, were selected.And the atomic parameters to reproduce experimental value of salvationenergy were determined on each of the molecules selected.

Finally, in FIG. 16D, based on the 4 atomic parameters 1610 determinedon atomic type NH₂ and averaged bond distance, the atomic parameterr_(NH2) 1611 was determined as r_(NH2)=0.2943*q+1.8561. As for each ofthe molecules numbered 3, 2, 6 and 8, because atomic parametersdetermined on each of the molecules and atomic parameters obtained bysubstitution of atomic charge to the linear function are different,calculation errors were calculated, using atomic parameter valuesobtained finally from the latter.

FIG. 17 shows comparison of the amount of calculation and calculationerror between in prior art explained in the above column “conventionaltechnique” and in the present embodiment. The abscissa axis in thedrawing is the amount of calculation defined as the calculation time1701 required for determination of atomic parameter using one computer,and the longitudinal axis is the calculation error 1702 defined asaverage value of absolute calculation error of each of the molecules.The plot of lozenge marks 1703 shows relation between amount ofcalculation and calculation error in the prior art, and the plot ofrectangular marks 1704 shows relation between amount of calculation andcalculation error in the present embodiment. In the present embodiment,molecules are sequentially selected and the calculation is completed ata time when all of the atomic parameters are determined. The amount ofcalculation required was 57 minutes, and a calculation error of about0.1 kcal/mol was obtained. Therefore, a method of the present embodimentshows about 9 times less amount of calculation required to attain ancalculation error of 0.1 kcal/mol, under calculation condition of thepresent embodiment.

FIG. 18 shows comparison of salvation energy prediction accuracy. On 6molecules, atomic parameters after iteration of 12 times by the priorart, and atomic parameters obtained by a method of the presentembodiment were applied respectively. The molecule 1801 selected has astructure similar to that of 10 molecules used in atomic parameterdetermination. In the drawing, the experimental value 1802, thecalculation error 1803 in the prior art, the calculation error 1804 inthe present embodiment and the averaged absolute error 1805 in bothmethods are shown. Because a method of the present embodiment alwaysdetermines atomic parameter one by one, it may be considered asapproximation to the atomic parameter determination method according tothe prior art. However, the averaged absolute error 1805 of the presentembodiment is a little smaller as compared with the conventional method.Therefore, the present embodiment that reduces the amount of calculationrequired for atomic parameter determination can be said to maintain alsoprediction accuracy of salvation energy. A method for expressing atomicparameter as a function of atomic charge or averaged bond distance isconsidered rather effective in calculation of solvation energy in highaccuracy.

Embodiment 3

Generalization of the atomic parameter determination method relevant tothis invention may be possible by substitution of a molecule with “ananalysis object”, atoms composing a molecule with “elements composing ananalysis object”, an atomic parameter with “an elemental parameter”,experimental value of solvation energy with simply “experimental value”and calculation value of solvation energy with simply “calculationvalue”. Explanation will be given below on a generalized parameterdetermination method in comparison, with the prior art with reference toFIG. 19 and FIG. 20.

FIG. 19 is a flowchart of the parameter determination method of thepresent embodiment. First of all, the convergence threshold τ 19011, theinformation necessary in calculation of analysis object and experimentalvalue 19012, and the elemental type and element attribute value 19013 ofeach element composing an analysis object are input from the inputapparatus 1901. Subsequently, in the initialization step 1902, theinitialization step 19021 of elemental parameter set by each of atomictypes and the sorting up step 19022 of all analysis objects by number ofundetermined elemental parameters are executed. In calculation orderlist generation step 1903, the analysis objects selection step 19031from analysis objects having the number of undetermined atomicparameters is 1, from a molecule containing undetermined atomicparameter and orders of arrangement and calculation of the analysisobjects selected are determined to execute the calculation ordergeneration step 19032 are executed. Then in the one-variable equationsolving step 1904, solving of one-valuable equation is iterated on ananalysis object on the top of calculation order list, until the amountof change of calculated value becomes below 1, and the undeterminedelemental parameter determination step 19041 and calculation order listupdate step 19042 are executed. In calculation order list terminationjudging step 19043, in the case where an analysis object is stillpresent on the top of calculation order list, procedure is returned tothe step 19041; in the case where an analysis object is not present anymore, procedure is forwarded to the elemental parameters update step1905. Next, in the elemental parameters update step 1905, as for anelemental type corresponding to determined elemental parameter, theelemental parameter expression formula update step 19051, which is afunction of value of elemental attribute, the sorting up step 19052 ofundetermined analysis objects by undetermined elemental parameters, thesorting down step 19053 of analysis objects with the identical number ofundetermined elemental parameters, by number of elemental parameters andthe undetermined analysis object update step 19054 are executed. Next,in the elemental parameter calculation termination judging step 1906,whether an undetermined analysis object is present or not, is judged. Inthe case where the undetermined analysis object is present, calculationorder list generation step 1903, the one-variable equation solving step1904 and the elemental parameters update step 1905 are iterated. In thecase where the undetermined analysis object is not present, calculationerror of each analysis object is calculated using the resultantelemental parameter, in the calculation error computing step 1907, andthe determined elemental parameters 19081 is output by the outputapparatus 1908.

FIG. 20 is details of processes in calculation order list generationstep, the one-variable equation solving step, and the elementalparameters update step, in the parameter determination method of thepresent embodiment. As an example, explanation will be given on thefirst and the second rounds of iterations of each of the steps, in thecase of the number of analysis objects of 9, and the number of elementaltype of 8. In the first round process 2002 to be executed in calculationorder list generation step 2001, the analysis object 20022 (analysisobject 8, analysis object 3 and analysis object 4) having the number ofundetermined elemental parameters of 1, are selected from analysisobjects arranged in sort up of the number of undetermined elementalparameters 20021 in advance. Calculation order of these analysis objectsis analysis object 8, analysis object 3 and analysis object 4, namelythe same as the arrangement order of the analysis objects, and thisorder is stored in calculation order list 20023. In the first roundprocess 2004 to be executed in the one-variable equation solving step2003, undetermined elemental parameter is determined based oncalculation order list. Because the first calculation is on analysisobject 8, calculated value is obtained first, using elemental parameterr_(a,8), and value of r_(a,8) is determined so as to be able toreproduce experimental value E₈. In this process, value that canreproduce experimental value is searched while changing r_(a,8),therefore, iterated solving of one-variable equation is required.Similar process is executed on the 2 selected analysis objects left. Inthe first round process 2006 to be executed in the atomic parametersupdate step 2005, expression formula of elemental parameter as afunction of value of elemental attribute, is updated on a, b and h thatare the elemental type corresponding to determined elemental parameter20061. For example, the elemental parameter 200062 of an elemental typea, can be expressed as r_(a)(q)=c₀+c₁p₁; where c₀ and c₁ arecoefficients. Then, undetermined value of elemental parameter classifiedto elemental type a is obtained by substitution of value elementalattribute p₁ into r_(a)(q)=c₀+c₁p₁. However, as for the element 20063,wherein elemental attribute value is apart from that of element used forthe parameter determination by certain threshold or more, there may bean option of not setting elemental parameter. The “value assigned”element 2010 is shown by a filled circle, and the value not assigned,namely the “undetermined element” 2011 is shown by an open circle. Then,6 analysis objects, 5, 6, 7, 2, 1 and 9, which are undetermined analysisobject at this time, are sorted up by the number 20064 of undeterminedelemental parameter. In addition, in the case where the number ofundetermined parameters is the same, the analysis objects are sort downby the number 20065 of elemental parameters. Here, analysis objectshaving the number of undetermined parameters of equal to or larger than1 become new undetermined molecules. Analysis object 2 has the number ofundetermined parameters of 0 at this moment, and thus is not used inelemental parameter determination. In the second round process 2007 tobe executed in calculation order list generation step 2001, the analysisobject 20072 (analysis object 5, and analysis object 6) having thenumber of undetermined elemental parameters 20071 of 1, are selectedfrom analysis objects arranged in advance. Calculation order of theseanalysis objects is analysis object 5, and analysis object 6, and thisorder is stored in calculation order list 20073. In the second roundprocess 2008 to be executed in the one-variable equation solving step2003, undetermined elemental parameter is determined based oncalculation order list. Calculated values are obtained first usingelemental parameter r_(a,5), under fixed value condition, andundetermined elemental parameter r_(d,5), to determined r_(d,5) so as toreproduce experimental value E₅. In this process, value that canreproduce experimental value is searched while changing only r_(d,5),therefore, process to be executed is iterated solving of one-variableequation, even for an analysis object composed of 2 elementalparameters. Similar process is executed on the 1 selected analysisobject left. In the second round process 2009 to be executed in theatomic parameters update step 2005, expression formula of elementalparameter, as a function of value of elemental attribute, is updated ona, b, h, d and e that are the elemental type 20091 corresponding todetermined elemental parameter. For example, the elemental parameter20092 of an elemental type a, is updated from r_(a)(q)=c₀+c₁p₁ tor_(a)(q)=c′₀+c′₁p₁. After updating expression formula and determinationof value of elemental parameter of an element classified to thecorresponding elemental type, re-arrangement operation of undeterminedanalysis objects is iterated in the same manner as the first round ofiteration. This process is iterated until an undetermined analysisobject is absent.

Finally, the amount of calculations obtained by a conventional parameterdetermination method and the parameter determination method according tothe present embodiment are compared. The amount of calculation in theprior art is described in expression 2. In the present embodiment,analysis objects are sequentially selected, and calculation is iteratedon each of the analysis objects until the amount of change of calculatedvalue becomes below energy convergence threshold. The number ofiteration is represented by I(n), which is different by an analysisobject, however, there are analysis objects not used in elementalparameter determination. Therefore, the amount of calculation iscalculated by “expression 8” using δ function which is defined 1 foranalysis objects used in elemental parameter determination, and 0 foranalysis objects not used. $\begin{matrix}{T_{invention} = {\sum\limits_{n = 1}^{N}{{\delta(n)}\left( {1 + {I(n)}} \right){f\left( {A(n)} \right)}}}} & \left( {{Expression}\quad 8} \right)\end{matrix}$

Comparison between expression 2 and expression 8 shows smaller amount ofcalculation in a method of present embodiment as compared with the priorart in view of three points. Firstly, calculation is executed on allanalysis objects in the prior art, while in the present embodiment,calculation is executed on a part of the analysis objects by presence ofthe 5 function, by which the amount of calculation is reduced. Secondly,the first term in the parenthesis at the right-hand side of the secondline of expression 2 is “I” in the prior art, while in the presentembodiment, the first term in the parenthesis at the right-hand side ofexpression 8 is “1”, by which the amount of calculation is reduced.Thirdly, the second term in the parenthesis is “I·p(n)” in the priorart, while in the present Embodiment, the first term in the parenthesisis “I(n)”. The number of iteration, I, required for solving of amatrix-equation as a multi-variable non-linear problem, is considered tobe larger than the the number of iteration “I(n)” required for solvingof a one-variable equation as a one-variable non-linear problem,therefore the amount of calculation in the present Embodiment isconsidered less.

Embodiment 4

Explanation will be given below on the atomic parameter determinationmethod under the fixed acceptable error condition relevant to thepresent embodiment of this invention, with reference to FIG. 21 and FIG.22.

FIG. 21 is a flowchart of the atomic parameter determination methodunder the fixed acceptable error condition. First of all, the acceptableenergy error ε 21011, the energy convergence threshold τ 21012, thethree-dimensional coordinate information and experimental value 21013 ofsalvation energy for a molecule and the atomic type, atomic charge, andaveraged bond distance 21014 for each atom composing a molecule areinput from the input apparatus 2101. Subsequently, in the initializationstep 2102, the initialization step 21021 of atomic parameter set by eachatomic type, and the sorting up step 21022 of all molecules by thenumber of undetermined atomic parameters are executed. Then, incalculation order list generation step 2103, the molecule selection step21031 of a molecule having the number of undetermined atomic parametersof equal to or less than 1, from a molecule containing undeterminedatomic parameter and the calculation order generation step 21032, bydetermination of sort order of selected molecules as calculation order,are executed. Then in the one-variable equation solving step 2104,solving of one-valuable equation is iterated, in the case where amolecule is judged to be included in the judgment step 21041 whether amolecule on the top of calculation order list contains undeterminedatomic parameters or not, until the amount of change of calculated valueof solvation energy becomes below τ, and the undetermined atomicparameter determination step 21042 is executed. Next, in spite of theresults of the judgment step 21041, the step 21043 calculating thedifference between calculated value and experimental value of themolecule by using determined atomic parameter, and the step 21044comparing absolute value of calculation error with acceptable error areexecuted, and in the case where the calculation error is over theacceptable energy error, the procedure is returned to the step 21041 viathe setting afresh step 21045 of undetermined atomic parameter, while inthe case where the calculation error is equal to or smaller than theacceptable energy error, calculation order list update step 21046 isexecuted. In calculation order list termination judging step 21047, inthe case where a molecule is still present on the top of calculationorder list, procedure is returned to the step 21041; however, in thecase where a molecule is not present any more, procedure is forwarded tothe atomic parameters update step 2105. Next, in the atomic parametersupdate step 2105, as for an atomic type corresponding to determinedatomic parameter, the atomic parameter expression formula update step21051, the equation being a function of atomic charge and averaged bonddistance, the step 21052 for tentatively determining values of atomicparameters for some or all of undetermined atoms, the sorting up step21053 of undetermined molecules by the number of undetermined atomicparameters, the sorting down step 21054 of molecules with the identicalnumber of undetermined atomic parameters by the number of atomicparameters and the undetermined molecule update step 21055 are executed.Next, in the atomic parameter calculation termination judging step 2106,whether an undetermined molecule is present or not, is judged. In thecase where the undetermined molecule is present, calculation order listgeneration step 2103, the one-variable equation solving step 2104 andthe atomic parameters update step 2105 are iterated. In the case wherethe undetermined molecule is not present, the value 21071 of determinedatomic parameters is output by the output apparatus 2107.

FIG. 22 is details of processes in calculation order list generationstep, the one-variable equation solving step, and the atomic parametersupdate step, in the atomic parameter determination method. As anexample, explanation will be given on the first and the second rounds ofiterations of each of the steps, in the case of the number of moleculesof 9, and the number of atomic types of 8. In the first round process2202 to be executed in calculation order list generation step 2201, themolecules 22022 (molecule 8, molecule 3 and molecule 4) having thenumber of undetermined atomic parameters of 1 or less are selected frommolecules sorted up by the number 22021 of undetermined atomicparameters in advance. Calculation order of these molecules is molecule8, molecule 3 and molecule 4, namely the same as the arrangement orderof the molecules, and this order is stored in calculation order list22023. In the first round process 2204 to be executed in theone-variable equation solving step 2203, undetermined atomic parameteris determined based on calculation order list. Because the firstcalculation is on molecule 8, salvation energy is calculated first,using atomic parameter r_(a,8), and value of r_(a,8) is determined so asto reproduce experimental value E₈. In this process, value that canreproduce experimental value is searched while changing r_(a,8),therefore, iterated solving of one-variable equation is required.Similar process is executed on the 2 selected molecules left. In thefirst round process 2206 to be executed in the atomic parameters updatestep 2205, expression formula of atomic parameter as a function ofatomic charge and averaged bond distance, is updated on a, b and h thatare the atomic type 22061 corresponding to determined atomic parameter.Expression formula of atomic parameter may be a function not havingvalue of an atomic attribute as a variable. For example, the atomicparameter 22062 of atomic type a can be expressed as r_(a)(q,1)=c₀=r_(a,8). Undetermined atomic parameter value classified to atomictype a is tentatively determined as r_(a)(q, 1)=c₀ However, as for theatom 22063, wherein atomic charge or averaged bond distance is apartfrom atomic charge or averaged bond distance of atom used in parameterdetermination, by certain threshold or more, there may be an option ofnot tentatively determining atomic parameter value. The atomic parameterdetermined atom 2210 is shown by a filled circle, the tentativelydetermined atom 2211 is shown by filled triangle, and the value notassigned, namely undetermined atom 2212 is shown by an open circle.Then, 6 molecules 5, 6, 7, 2, 1 and 9, which are undetermined moleculesat this time, are sorted up by the number 22064 of undetermined atomicparameters. In addition, in the case where the number of undeterminedparameters is the same, the molecules are sorted down by the number22065 of atomic parameters. Here, all of the 6 molecules become newlyundetermined molecules. In the second round process 2207 to be executedin calculation order list generation step 2201, the molecule 22072(molecule 2, molecule 5, and molecule 6) having the number 22071 ofundetermined atomic parameters of 1 or less, are selected from moleculesarranged in advance. Calculation order of these molecules is molecule 2,molecule 5, and molecule 6, and this order is stored in calculationorder list 22073. In the Second round process 2208 to be executed in theone-variable equation solving step 2203, undetermined atomic parameteris determined based on calculation order list. Explanation will be givenparticularly on molecule 2 having no undetermined parameters. Firstly,salvation energy is calculated, using atomic parameter given. Then,whether absolute value of calculation error, defined as differencebetween calculated value and experimental value, is below acceptableenergy error or not, is confirmed. In the case where absolute value ofcalculation error is equal to or larger than acceptable energy error,only one of the 2 atomic parameters r_(a,2) and r_(h,2) contained inmolecule 2 is set newly as an undetermined atomic parameter. Atomicparameter to be selected is one having larger solvation energy gradientrelative to change in both atomic parameters. In the case where theselected parameter is r_(a,2), value of r_(a,2) is determined so as toreproduce experimental value E₂. In the Second round process 2209 to beexecuted in the atomic parameters update step 2205, expression formulaof atomic parameter, as a function of atomic charge and averaged bonddistance, is updated on a, b, h, d and e that are the atomic type 22091corresponding to determined atomic parameter. For example, the atomicparameter 22092 of atomic type “a” was r_(a)(q, 1)=c₀=r_(a,8), however,because use of newly determined value of r_(a,2) is also required foratomic parameter of an atomic type “a”, based on the calculation resultof molecule 2, use of more complicated function form is required. Forexample, it may be updated to r_(a)(q, 1)=c′₀+c′₁q. After updatingexpression formula and determination of atomic parameter value of anatom classified to the corresponding atomic type, re-arrangementoperation of undetermined molecules is iterated in the same manner asthe first round of iteration. This process is iterated until anundetermined molecule is absent.

Explanation will specifically be given on a mounting example of processin relation to a part different from process in embodiment 1, among thesteps of a flowchart of the atomic parameter determination method underthe fixed acceptable error condition, shown by FIG. 21.

FIG. 23 is details of calculation order list update step. At the time ofthe start 2301, calculation of a molecule on the top of calculationorder list is over. In the new setting judgment step 2302 ofundetermined parameter, whether a process for newly setting one of thetentatively determined atomic parameters as an undetermined atomicparameter is terminated or not, is judged in a determination process ofundetermined parameter of the molecule. In the case where thedetermination results is “yes”, whole delete process 2303 of acalculation order list is executed; while the results is “no”, thedelete process 2304 of molecule on the top from a calculation order listand sequentially move forward the residual molecules is executed. Then,in calculation order list termination judging step 2305, whether thecalculation list is empty or not, is judged; in the case 2306 of empty,process goes forward to the atomic parameters update step; in the case2307 of not empty 2307, process returns to the undetermined atomicparameter determination step.

Explanation will be given on the atomic parameter, r_(t)(q, 1), updatestep 21051 of atomic type corresponding to determined atomic parameter,using FIGS. 24A and 24B, and FIGS. 25A and 25B.

FIG. 24A shows an example of atomic parameter update in the case thatthe atomic parameter value 2401 is expressed by a function of value 2402of an atomic attribute such as atomic charge as a variable. A filledcircle in the drawing shows the “value assigned” atom 2403, and an opencircle shows the “value not assigned” atom 2404. First of all, by usingthe “value assigned” atom 2403, the linear function 2405 that correlatesatomic parameter value and value of an atomic attribute is defined.Then, the value 2406 of an atomic attribute of a “value not assigned”atom is substituted to a linear function to tentatively determine atomicparameter value.

FIG. 24B shows an example of execution result of the step forpreparation of calculation order list, the step for solving aone-variable equation, and the step for atomic parameter-updating, usingtentatively determined atomic parameter value. There are the atom 2407having value of tentatively determined atomic parameter set asdetermined value as it is and the atom 2408 having re-determined atomicparameter, after tentatively determined atomic parameter value being setas undetermined atomic parameter. Description of atomic parameter valuesof these atoms by a linear function of value of an atomic attributevaries already determined atomic parameter values and also salvationenergy of molecules with already determined atomic parameter. However,definition of the three regions 2409 based on value of an atomicattribute and definition of the linear function 2410 relative to eachregion can express by a function using newly determined atomicparameters, without changing salvation energy of molecules with alreadydetermined atomic parameter.

FIG. 25A shows an example of atomic parameter update in the case thatthe atomic parameter value 2501 is expressed by a function of values oftwo atomic attributes such as the atomic charge 2502 and the averagedbond distance 2503 as variables. A filled circle in the drawing showsthe “value assigned” atom 2504, and an open circle shows the “value notassigned” atom 2505. First of all, by using the “value assigned” atom2504, the linear function correlating atomic parameter value with valueof an atomic attribute 2506 is defined. Then, atomic charge and theaveraged bond distance 2507 of the “value not assigned” atom aresubstituted in a linear function to tentatively determine atomicparameter value.

FIG. 25B shows an example of execution result of the step for preparingcalculation order list, the step for solving a one-variable equation,and the step for updating atomic parameter, using tentatively determinedatomic parameter value. There exist the atom 2508, which the tentativelydetermined value became the determined value as it is, and the atom2509, which the tentatively determined value was set as undeterminedatomic parameter, and atomic parameter was re-determined. Description ofvalues of atomic parameters of these atoms by a linear function ofvalues of atomic attributes varies already determined atomic parametervalues, and also salvation energy of molecules with already determinedatomic parameter. However, definition of the two regions 2510 on a planeformed by atomic charge and averaged bond distance, and definition ofthe linear function 2511 defined in each region based on value of anatomic attribute can express by a function using newly determined atomicparameters, without changing salvation energy of molecules with alreadydetermined atomic parameter.

Finally, the amount of calculations in a conventional atomic parameterdetermination method and the atomic parameter determination methodaccording to the present embodiment are compared. The amount ofcalculation in the prior art is described in expression 2. In thepresent embodiment, molecules are sequentially selected, and calculationis iterated on each of the molecules until the amount of change ofcalculated value of salvation energy becomes below energy convergencethreshold. The number of iteration is represented by I(n), which isdifferent by a molecule, however, there are also molecules having anundetermined atomic parameter number of 0. Therefore, the amount ofcalculation is calculated by “expression 9” using δ function, which isdefined 1 for molecules requiring determination process of undeterminedatomic parameter, and 0 for molecules not requiring the process.$\begin{matrix}{T_{invention} = {\sum\limits_{n = 1}^{N}{\left( {1 + {{I(n)} \cdot {\delta(n)}}} \right){f\left( {A(n)} \right)}}}} & \left( {{Expression}\quad 9} \right)\end{matrix}$

Comparison between expression 2 and expression 9 shows smaller amount ofcalculation in a method of present embodiment as compared with the priorart in view of two points. Firstly, the first term in the parenthesis atthe right-hand side of the second line of expression 2 is “I” in theprior art, while in the present Embodiment, the first term in theparenthesis is “1”, by which the amount of calculation is reduced.Secondly, the second term in the parenthesis is “I·p(n)” in the priorart, while in the present Embodiment, the first term in the parenthesisis “I(n)·δ(n)”, which reduces the amount of calculation by 2 reasons.One is that the number of iteration, I, required for solving of amatrix-equation as a multi-variable non-linear problem, is considered tobe larger than the number of iteration “I(n)” required for solving of aone-variable equation as a one-variable non-linear problem. The secondis that minimal value of the number of atomic type p(n) included inmolecule n is 1, but δ function takes a value of 0 or 1.

Furthermore, difference of the amount of calculation between in theprior art and in a method of the present embodiment increases whennumber of molecules N is large. Explanation will be given below onreason therefor.

In a method of the present embodiment, atomic parameter is expressed bya function having atomic charge and averaged bond distance as variables.Form of the function becomes complicated during the processes ofselection of a molecule and determination of undetermined parameters.However, range of atomic charge and averaged bond distance that can betaken by an atom is finite. Therefore, after sophistication of functionform to a certain degree, it is considered that atomic parameter valuecan tentatively be determined in high accuracy for every combination ofatomic charge and averaged bond distance. Therefore, in the case wherethe number of molecules is large, as for a molecule selected at thefinal phase of parameter determination process, probability of tentativedetermination of atomic parameter value in high accuracy becomes highfor all atoms composing the molecule. This corresponds to the fact that,in corresponding the summation order on the molecule n in expression 9,with the calculation order of molecules used in atomic parameterdetermination, probability of δ(n)=1 is high when n is small, andprobability of δ(n)=0 is high with increase of n. Small molecule numberN is considered not to increase probability of δ(n)=0 so much, even atthe final phase of parameter determination process, but large moleculenumber N is considered to increase probability of δ(n)=0.

In addition, a method of the present Embodiment has effect of reducingcalculation number of a large molecule. Discussion was made above onsmall and large of constant term part, which is multiplied to f(A(n)),in comparison of expression 2 with expression 9, which show the amountof calculation required for atomic parameter determination, however,because f(A(n)) is a power function of atomic number A(n) of themolecule n, reduction of calculation number of a molecule with largeA(n) is more important. Selection order of molecules in the presentembodiment is, in general, “a small molecule early and a large moleculelater”; a firstly selected molecule is a molecule having an atomicparameter number of 1; a molecule having a non-hydrogen atom number of 1such as methane, ammonia or the like corresponds to this type. Althoughthere is an exception that a benzene molecule has an atomic parameternumber of 1, due to having high symmetry, in spite of containing 6carbon atoms, usually a small molecule is preferentially selected, and alarge molecule is selected at the final phase of parameter determinationprocess. As discussed above, probability of δ(n)=0 is high at the finalphase of parameter determination process; namely probability thatcalculation iteration is required is high, to determine undeterminedatomic parameter.

Summary of the above discussion will be given in FIG. 26. It is assumedthat the number of molecules N used in the atomic parameterdetermination is assumed sufficiently large, and in addition, moleculesare arranged in calculation order in the present embodiment, relative tosummation symbol of expression 2 and expression 9. In spite of the earlycalculation stage 2601, namely when n is small, and the last calculationstage 2602, namely when n is large, the amount 2603 of calculation forthe molecule n in the prior art is constant. Because it is an iterativecalculation method, in each time, for solvation energy and solvationenergy gradient relative to change in atomic parameter value, for allthe atoms, change in calculation order of molecules does not effect theamount of calculation. On the other hand, because the amount 2604 ofcalculation for the molecule n in embodiment of this invention has highprobability of execution of determination process of undeterminedparameter at the early phase of calculation, value of δ(n)=1 is taken inexpression 9. However, because in the early calculation stage 2601,probability is high that a selected molecule is small, and thus theamount f(A(n)) 2605 of calculation required for calculation of solvationenergy in one time is small as result. The amount 2604 of calculationfor the molecule n at the last calculation stage, value of δ(n)=0 istaken in expression 9, because possibility is high that atomicparameters are tentatively determined for all atoms composing amolecule. Because in the last calculation stage 2602, probability ishigh that of a selected molecule is large, the amount f(A(n)) 2605 ofcalculation of solvent energy in one time, is large as result.

Embodiment 5

The present embodiment shows atomic parameter determination result underthe fixed acceptable error condition using 63 molecules. Contents ofmolecules used in atomic parameter determination include 18 cations, 11anions and 34 neutral molecules. The acceptable error was set 1.4kcal/mol for the cations and the anions, and 0.20 kcal/mol for theneutral molecules. As a result, 57 atomic parameters were obtained.

FIG. 27 is comparison of the amount of calculation in Embodiment of thisinvention and in prior art, in the atomic parameter determination methodusing 63 molecules. In the present embodiment, the averaged number 2701of iteration of calculation of solvation energy of each of the moleculesin sequential determination process of 57 atomic parameters was 3.32times. In addition, the amount 2702 of calculation, defined bycalculation time required for atomic parameter determination using onecomputer, was about 504 minutes. Calculation time in using a gradientmatrix could not actually be measured, however, the lower bound 2703 ofthe amount of calculation was estimated as 3183 minutes by the followingcalculation. Firstly, in expression 6, there is actually measured valueof the amount f(A(n)) of calculation, required for salvation energycalculation in one time, on each of molecules n. In addition, the numberof atomic type contained in each of the molecules was determined usingdefinition of atomic type, by Tomasi et al, (V. Barone, M. Cossi and J.Tomasi, “A new definition of cavities for the computation of salvationfree energies by the polarizable continuum model”, Journal of ChemicalPhysics, Vol. 107, 3210, (1997)]. Here, unknown value left is only thenumber of iteration I. Minimization of objective function defined by amatrix-equation is a multi-variable non-linear problem, and many methodsfor reducing the number of iteration required for solving are present.However, the number of iteration I is considered more than 3.32 timesthat is averaged value of the number of iteration required for solving aone-variable equation. Accordingly, the number of iteration wasestimated to be the minimal integer I=4, equal to or larger than 3.32.From the result, the atomic parameter determination method of thepresent embodiment can be said to provide the amount of calculationabout 6.3 times less as a minimum, as compared with the prior art. Inthe prior art, it is required that atomic type is re-defined to iteratewhole process of atomic parameter determination, when desired accuracyis not obtained, therefore, when this number of iteration is taken as k,difference in the amount of calculation becomes 6.3 k times.

Embodiment 6

Generalization of the atomic parameter determination method by the fixedacceptable error condition, of the present embodiment, is possible bysubstitution of a molecule with “an analysis object”, atoms composing amolecule with “elements composing an analysis object”, an atomicparameter with “an elemental parameter”, experimental value of salvationenergy with simply “experimental value”, and calculation value ofsolvation energy with simply “calculation value”. Explanation will begiven below on the parameter determination method by the fixedgeneralized acceptable error condition, with reference to FIG. 28 andFIG. 29.

FIG. 28 is a flowchart of simulation parameter determination methodunder the fixed acceptable error condition. First of all, the acceptableerror ε 28011, the convergence threshold τ 28012, the informationnecessary in calculation of an analysis object and experimental value28013 and the elemental type and element attribute value 28014 for eachelement composing an analysis object are input from the input apparatus2801. Subsequently, in the initialization step 2802, set by each ofatomic types, the elemental parameter initialization step 28021 and thesorting up step 28022 of all analysis objects by the number ofundetermined elemental parameters are executed. In calculation orderlist generation step 2803, the selection step 28031 of analysis objectshaving undetermined elemental parameter number of equal to or less than1, from analysis objects containing undetermined elemental parameter,and orders of arrangement and calculation of the analysis objectsselected are determined to execute calculation order list generationstep 28032 are executed. Then in the one-variable equation solving step2804, in the case where “inclusion” is judged, in the judgment step28041 on whether an analysis object on the top of a calculation orderlist contains undetermined elemental parameter or not, the solving of aone-valuable equation is iterated on an analysis object on the top ofcalculation order list, until the amount of change of calculated valuebecomes below τ, and the undetermined elemental parameter determinationstep 28042 is executed. Then in spite of the result of the judgment step28041, the calculation error computing step 28043, as difference betweencalculation value of the analysis object using elemental parameter, andexperimental value, and the comparing step 28404 of calculation errorwith acceptable error are executed, and in the case where thecalculation error is over the acceptable error, procedure is returned tothe step 28041 via the setting afresh step 28045 of undeterminedelemental parameter for one of tentatively determined atomic parameters;in the case where the calculation error is equal to or less than theacceptable error, calculation order list update step 28046 is executed.In calculation order list termination judging step 28047, in the casewhere an analysis object is still present on the top of calculationorder list, procedure is returned to the step 28041; in the case wherean analysis object is not present any more, procedure is forwarded tothe elemental parameters update step 2805. Next, in the elementalparameters update step 2805, as for an elemental type corresponding todetermined elemental parameter, the elemental parameter expressionformula update step 28051, the equation being a function of value ofelemental attribute, the tentatively determining step 28052 of some orall of values of elemental parameters of an undetermined element, thesorting up step 28053 of undetermined analysis objects by number ofundetermined elemental parameters, the sorting down step 28054 ofanalysis objects with the identical number of undetermined elementalparameters by number of elemental parameters and the undeterminedanalysis object update step 28055 are executed. In the elementalparameter calculation termination judging step 2806, whether anundetermined analysis object is still present or not, is judged. In thecase where the undetermined analysis object is present, calculationorder list generation step 2803, the one-variable equation solving step2804 and the elemental parameters update step 2805 are iterated; and inthe case where the undetermined analysis object is not present, thedetermined elemental parameters 28071 is output by the output apparatus2807.

FIG. 29 is details of processes in calculation order list generationstep, the one-variable equation solving step, and the elementalparameters update step, in an elemental parameter determination method.As an example, explanation will be given on the first and the secondrounds of iterations of each of the steps, in the case of the number ofanalysis objects of 9, and the number of elemental type of 8. In thefirst round process 2902 to be executed in calculation order listgeneration step 2901, the analysis object 29022 (analysis object 8,analysis object 3 and analysis object 4) having the number ofundetermined elemental parameters of 1 or less are selected fromanalysis objects sorted up by the number 29021 of undetermined elementalparameters in advance. Calculation order of these analysis objects isanalysis object 8, analysis object 3 and analysis object 4, namely thesame as the arrangement order of the analysis objects, and this order isstored in calculation order list 29023. In the first round process 2904to be executed in the one-variable equation solving step 2903,undetermined elemental parameter is determined based on calculationorder list. Because the first calculation is on analysis object 8,calculated value is obtained, using elemental parameter r_(a,8), andvalue of r_(a,8) is determined so as to reproduce experimental value E₈.In this process, value that can reproduce experimental value is searchedwhile changing r_(a,8), therefore, iterated solving of a one-variableequation is required. Similar process is executed on the 2 selectedanalysis objects left. In the first round process 2906 to be executed inthe elemental parameters update step 2905, expression formula ofelemental parameter as a function of values of elemental attributes, isupdated on a, b and h that are the elemental type 29061 corresponding todetermined elemental parameter. Expression formula of elementalparameter may be a function not having value of elemental attribute as avariable. For example, the elemental parameter 29062 of an elementaltype a, can be expressed as r_(a)(p₁,p₂)=c₀=r_(a,8). Then, undeterminedelemental parameter value classified to elemental type a is obtained asr_(a)(p₁,p₂)=c₀. However, on the element 29063, wherein elementalattribute value is apart from that of other element belonging to theidentical elemental type by certain threshold or more, there may be anoption of not tentatively determine elemental parameter. The element2910 having determined value of elemental parameter is shown by a filledcircle, tentatively determined element 2911 is shown by a filledtriangle, and the value not assigned, namely the undetermined element2912 is shown by an open circle. Then, at this time, 6 analysis objects5, 6, 7, 2, 1 and 9 are re-arranged in sort up of the number 29064 ofundetermined elemental parameter. In addition, in the case where thenumber of undetermined parameters is the same, the analysis objects arere-sorted down by the number 29065 of elemental parameters. Here, all ofthese 6 analysis objects become undetermined analysis objects newly. Inthe second round process 2907 to be executed in calculation order listgeneration step 2901, the analysis object, having the number 29072(analysis object 2, analysis object 5 and analysis object 6) ofundetermined elemental parameters 29071 of 1 or less, are selected fromanalysis objects arranged in advance. Calculation order of theseanalysis objects is analysis object 2, analysis object 5 and analysisobject 6, and this order is stored in calculation order list 29073. Inthe second round process 2908 to be executed in the one-variableequation solving step 2903, undetermined elemental parameter isdetermined based on calculation order list. Explanation willparticularly be given on analysis object 2 not having undeterminedparameter. First of all, calculation value is obtained using anelemental parameter given. Then, whether absolute value of calculationerror, defined as difference between calculated value and experimentalvalue, is below acceptable error or not, is confirmed. In the case whereabsolute value of calculation error is equal to or larger thanacceptable error, any one of the 2 elemental parameters, r_(a,2), andr_(h,2), contained in analysis object 2 is set newly as undeterminedelemental parameter. The elemental parameter to be selected should beone having larger gradient of calculation value relative to change inboth elemental parameters. In the case where the selected parameter isr_(a,2), value of r_(a,2) is determined so as to reproduce experimentalvalue E₂. In the second round process 2909 to be executed in the atomicparameters update step 2905, expression formula of elemental parameter,as a function of value of elemental attribute, is updated on a, b, h, dand e that are the elemental type 29091 corresponding to determinedelemental parameter. For example, the elemental parameter 29092 of anelemental type a, is updated from r_(a)(p₁,p₂)=c₀=r_(a,8), however, useof more complicated function form is required, because use of newlydetermined value of r_(a,2) is required as an elemental parameter ofelemental type a, based on calculation result of analysis object 2. Forexample, updating to r_(a)(p₁,p₂)=c′₀+c′₁p₁ may be allowed. Afterupdating expression formula and determination of value of elementalparameter of an element classified to the corresponding elemental type,re-arrangement operation of undetermined analysis objects is iterated inthe same manner as the first round of iteration. This process isiterated until an undetermined analysis object is absent.

Finally, the amount of calculations in the parameter determinationmethod by the prior art and the parameter determination method accordingto the present embodiment are compared. The amount of calculation in theprior art is described in expression 2. In the present embodiment,analysis objects are sequentially selected, and calculation is iteratedon each of the analysis objects until the amount of change of calculatedvalue becomes below convergence threshold. The number of iteration isexpressed by I(n), which is different by an analysis object, however,there are analysis objects having an undetermined elemental parameternumber of 0. Therefore, the amount of calculation is calculated by“expression 10” using δ function, which is defined 1 for analysisobjects requiring undetermined elemental parameter determinationprocess, and 0 for analysis objects not required the process.$\begin{matrix}{T_{invention} = {\sum\limits_{n = 1}^{N}{\left( {1 + {{I(n)} \cdot {\delta(n)}}} \right){f\left( {A(n)} \right)}}}} & \left( {{Expression}\quad 10} \right)\end{matrix}$

Comparison between expression 2 and expression 10 shows smaller amountof calculation in a method of present embodiment as compared with theprior art in view of 2 points. Firstly, the first term in theparenthesis at the right-hand side of the second line of expression 2 is“I” in the prior art, while in the present Embodiment, the first term inthe parenthesis is “1”, by which the amount of calculation is reduced.Secondly, the second term in the parenthesis is “I·p(n)” in the priorart, while in the present Embodiment, the first term is “I(n)·ε(n)”,therefore, the amount of calculation is less by the following tworeasons. One is that the number of iteration, I, required for solving amatrix-equation as a multi-variable non-linear problem, is considered tobe larger than the number “I(n)” of iteration required for solving aone-variable equation as a one-variable non-linear problem. Second isthat minimum value of the number p(n) of elemental type contained inanalysis object n is 1; on the other hand, 6 function takes a value ofeither 0 or 1.

Embodiment 7

Explanation will be given on an example of mounting example of userinterface accompanying with the atomic parameter determination method,using FIG. 30 to FIG. 33.

FIG. 30 is a flowchart in the atomic parameter determination methodincluding the information display step. Explanation was already given indetail, in embodiment 1 and embodiment 4, on sections not relating toinformation display, therefore such explanation is simplified here. Inthe atomic parameter determination according to the present embodiment,input step 3001 and the initialization step 3002 are executed first.Then, in calculation order list generation step 3003, a calculationorder list is displayed on a screen by calculation order list displaystep 30032 via the inner process 30031. A user may add change in thecalculation order displayed on a screen, and finally settles thecalculation order. In the calculation progress display step 30033,outline of progress of atomic parameter calculation and a calculationprogress by a molecule are displayed. Then, the equation solving step3004 is executed. In the atomic parameters update step 3005, via theinner process 30051, in the atomic parameter display step 30052, atomicparameter is displayed using space formed by atomic parameter, atomiccharge and averaged bond distance. Finally, the output step 3007 isexecuted via the termination judging step 3006. In the above flowchart,sections relating to information display are 3 parts; calculation orderlist display step 30032, the calculation progress display step 30033 andthe atomic parameter display step 30052.

FIG. 31 is an example of screen display in calculation order listdisplay step. Calculation order list tab 31011 is selected among 3display objects contained in the display object displaying tab 3101.Display view of calculation order list is divided into 3; namely, thecalculation order display region 3102, the distribution diagram displayregion 3103 and the molecular structure map display region 3104. At theearly display stage, calculation order list 31021 is displayed in thecalculation order display region 3102. These tables can be selected lineby line, and in this drawing molecule 5 is in a selected status.Calculation order of selected molecules can be adjusted by the up-arrowbutton 31022 or the down-arrow button 31023. In addition, by the deletebutton 31024, “no-calculation” choice on the selected molecule is alsopossible. When a user pushes the confirm button 31025, calculation orderis settled. Supporting data for a user to judge change in calculationorder includes a distribution chart and a molecular structure chart. Inthe distribution diagram display region 3103, an example of atomicdistribution chart is shown where undetermined atomic parameters ofmolecule 5 are classified into atomic type d, which belongs. Atoms areplotted on a plane formed by atomic charge and averaged bond distance.The plot has a different shape or a pattern by reflecting a status of“value assigned”, “value not assigned” or the like of atomic parametercorresponding to each atom, or a selection status in calculation orderlist 31021. In the present embodiment, atoms classified to atomic type dare only 2, and both are plotted at positions apart on a plane;therefore, it is visually understood that even if one atomic parameteris determined, the other atomic parameter cannot necessarily betentatively determined in high accuracy based on thus determined atomicparameter. Based on this information, a user may choose to descendcalculation priority order of molecule 5. In the molecular structure mapdisplay region 3104, a molecular conformation and a sphere having radiuscorresponding to atomic parameter value of each molecule forming themolecule are displayed in an overlapped way. The sphere is displayedalso here with a different pattern by reflecting a status of “valueassigned”, “value not assigned” or the like of atomic parametercorresponding to each atom, or a selection status in calculation orderlist 31021. Molecule 5 is a molecule composed of 3 non-hydrogen atoms,and two of them are understood to be equivalent in view of symmetry.Atomic parameter value for the atom X has tentatively been determinedalready, and value has been assigned. On the other hand, it is visuallyunderstood that atomic parameter value for the atom Y will be determinedfrom now. Atoms in a molecule displayed in a plot in the distributiondiagram display region 3103 or in the molecular structure map displayregion 3104 may also be selected. When a plot is selected a structure ofa molecule to which the corresponding atom belongs is displayed in themolecular structure map display region 3104. In addition, when an atomis selected, a distribution chart of an atom related to correspondingatomic type is displayed in the distribution diagram display region3103. These functions are capable of furnishing information of othermolecules directly relating to parameter determination of molecule 5noticed.

FIG. 32 is an example of screen display in the calculation progressdisplay step. The progress tab 32011 is selected among 3 display objectscontained in the display object displaying tab 3201. Display view of acalculation progress is divided into the display region of summary of anatomic parameter calculation progress 3202 and the display region of anatomic parameter calculation progress for each molecule 3203. In thedisplay region of summary of an atomic parameter calculation progress3202, summing up result of a calculation status of a molecule such as“determined”, “in progress” or “undetermined”, and calculation elapsedtime is displayed. In addition, in the display region of an atomicparameter calculation progress for each molecule 3203, a calculationstatus of each molecule, molecular ID, atomic parameter number andundetermined atomic parameter number are displayed. From these sets ofinformation, a progress degree of parameter determination procedure canbe understood.

FIG. 33 is an example of screen display in the atomic parameter displaystep. The atomic parameter tab 33011 is selected among 3 display objectscontained in the display object displaying tab 3301. Display view ofatomic parameter is divided into the display region of the atomicparameter determination status of each atomic type 3302, and the displayregion of atomic parameter value 3303. At the early display stage,atomic type, total atom number belonging to the corresponding atomictype, atom number with atomic parameter determined, tentativelydetermined atom number and undetermined atom number are displayed in aTable form in the display region of the atomic parameter determinationstatus of each atomic type 3302. These tables can be selected by eachline, and in this drawing, atomic type a is in a selected status. In thedisplay region of atomic parameter value 3303, atomic parameter value inselected atomic type is displayed using space formed by atomicparameter, atomic charge and averaged bond distance. By graphic displayof atomic parameter value in three-dimensional space, dependence ofatomic parameter on atomic charge and averaged bond distance canintuitively be understood.

Description will be given below on effect of the above-describedembodiments.

By a system to preferentially select a molecule containing atomicparameter that can be determined in high certainty, and to controlcalculation order of solvation energy relating to selected molecule bycalculation order list, according to the present embodiment, atomicparameter determination is possible by smaller amount of calculation ascompared with the prior art.

In embodiment 1, determination possibility of atomic parameter used incalculation of solvation energy of a molecule, by smaller amount ofcalculation as compared with the prior art was shown. In embodiment 2,by demonstration calculation using 10 molecules, it was shown that theatomic parameter determination method of the present embodiment iscapable of determining atomic parameter with equivalent accuracy, bysmaller amount of calculation as compared with a method based on theprior art. In embodiment 4, it was shown that atomic parameter used incalculation of salvation energy of a molecule can be determined bysmaller amount of calculation as compared with the prior art, and thatcalculation error can also be controlled by the atomic parameterdetermination method with acceptable error fixed. In embodiment 5, itwas shown, by demonstration calculation using 63 molecules, that theamount of calculation required for the atomic parameter determinationmethod under the fixed acceptable error condition is smaller thanestimation level of the amount of calculation required for a methodbased on the prior art.

In addition, by a system to preferential select an analysis objectcontaining parameter that can be determined in high certainty, and tocontrol calculation relating to analysis objects selected, bycalculation order list, according to the present embodiment, atomicparameter determination is possible by smaller amount of calculation ascompared with the prior art.

The embodiment of this invention is capable of dividing calculationobject into elements, and defining value of attribute of each of theelements, and thus applicable to the case where evaluation of calculatedvalue or gradient relative to parameter change of calculated value isthe rate determining step of calculation.

Furthermore, embodiment of this invention is capable of reflecting userknowledge to parameter determination, because determination process ofcalculation order of analysis objects, as important elements of theparameter determination method, is visualized, and function that a usercan change calculation order is provided. In embodiment 7, a displayexample of supporting data for a user to judge change in calculationorder was shown.

It should be noted, description of reference numerals is as follows.

-   101: Calculation object molecule-   102: Water-based solvent-   103: Space occupied by a molecule-   104: Space occupied by dielectrics-   105: Sphere arranged on an atom-   106: Radius of a sphere arranged on an atom-   201: Input apparatus-   2011: Input of energy convergence threshold τ-   2012: Input of a structure and experimental value of salvation    energy of a molecule-   2013: Input of atomic type for each atom composing a molecule-   202: The atomic parameter initialization step-   203: The matrix generation step-   204: The matrix-equation solving step-   205: The atomic parameters update step-   206: The atomic parameter calculation termination-judging step-   207: Output apparatus-   2071: Output of converged atomic parameter value-   301: The matrix generation step-   302: Process to be executed in the matrix generation step-   3021: Solvation energies of all molecules,-   3022: Solvation energy gradient of all molecules relative to change    in each atomic parameter-   3023: Matrix composed of molecular number as the number of line, and    (the number of atomic type +1) as the number of columnt-   3024: Matrix element-   303: The matrix-equation solving step-   304: Process to be executed in the matrix-equation solving step-   3041: Matrix-   3042: Solution vector having the number of element of (the number of    atomic type +1)-   3043: Experimental value vector of solvation energy, having the same    element number as the number of molecule-   3044: Objective function-   305: The atomic parameters update step-   306: Process to be executed in the atomic parameters update step-   3061: New atomic parameter vector-   3062: Atomic parameter vector before update-   3063: Vector deleted only top element from the solution vector    obtained in the matrix equation-solving step 303-   401: Atomic type-   402: The resultant atomic parameter value-   403: Atomic type that each atom contains-   501: Calculation amount-   502: Calculation error-   503: Plot of lozenge marks-   601: Input apparatus-   6011: Input of convergence threshold τ-   6012: Input of necessary information and experimental value for    calculation of analysis object-   6013: Input of an elemental type for each element composing an    analysis object-   602: The elemental parameter initialization step-   603: The matrix generation step-   604: The matrix-equation solving step-   605: The elemental parameters update step-   606: The elemental parameter calculation termination-judging step-   607: Output apparatus-   6071: Output of converged elemental parameter-   701: The matrix generation step-   702: Process to be executed in the matrix generation step-   7021: Calculated value of all analysis objects-   7022: Gradients of calculated value of all analysis objects to    change of each elemental parameter-   7023: Matrix composed of analysis object number as the number of    line, and (elemental type number +1) as the number of columnt-   7024: Matrix element-   703: The matrix-equation solving step-   704: Process to be executed in the matrix-equation solving step-   7041: Matrix-   7042: Solution vector having the number of element of (elemental    type number +1)-   7043: Experimental value vector having the same elemental number as    analysis object number-   7044: Objective function-   705: The elemental parameters update step-   706: Process to be executed in the elemental parameters update step-   7061: New elemental parameter vector-   7062: Elemental parameter vector before update-   7063: Vector deleted only top element from the solution vector    obtained in the matrix-equation solving step 303-   801: Input apparatus-   8011: Input of energy convergence threshold τ-   8012: Input of three-dimensional coordinate information and    experimental value of salvation energy for molecule-   8013: Input of atomic type, atomic charge, and averaged bond    distance for each atom-   802: The initialization step-   8021: The initialization step of atomic parameter-   8022: The sorting up step of all the molecules by the number of    undetermined atomic parameters-   803: Calculation order list generation step-   8031: The molecule selection step-   8032: The calculation order determination step-   804: The one-variable equation solving step-   8041: The undetermined atomic parameter determination step-   8042: Calculation order list update step-   8043: Calculation order list termination judging step-   805: The atomic parameters update step-   8051: The atomic parameter expression formula update step-   8052: The sorting up step of undetermined molecules by the number of    undetermined atomic parameters-   8053: The sorting down step of molecules with the identical number    of undetermined atomic parameters by the number of atomic parameters-   8054: The undetermined molecule update step-   806: The atomic parameter calculation termination judging step-   807: The calculation error computing step-   808: Output apparatus-   8081: Output of determined atomic parameter value-   901: Calculation order list generation step-   902: First round process to be executed in calculation order list    generation step-   9021: The number of undetermined atomic parameters-   9022: Molecule having the number of undetermined atomic parameter of    1-   9023: Calculation order list-   903: The one-variable equation solving step-   904: First round process to be executed in the one-variable equation    solving step-   905: The atomic parameters update step-   906: First round process to be executed in the atomic parameters    update step-   9061: Atomic type corresponding to determined atomic parameter-   9062: Atomic parameter of the atomic type a-   9063: Atom, wherein atomic charge is apart from that of other atom    belonging to the identical atomic type by certain threshold or more-   9064: The number of undetermined atomic parameters-   9065: The number of atomic parameters-   907: Second round process to be executed in calculation order list    generation step-   9071: The number of undetermined atomic parameters-   9072: Molecule having the number of undetermined atomic parameters    of 1-   9073: Calculation order list-   908: Second round process to be executed in the one-variable    equation solving step-   909: Second round process to be executed in the atomic parameters    update step-   9091: Atomic type corresponding to determined atomic parameter-   9092: Atomic parameter of atomic type a-   910: “Value assigned” atom-   911: “Value not assigned” (undetermined) atom-   1001: Three-dimensional coordinate information of the molecule-   1002: Structure of para-xylene molecule-   1003: Experimental value of salvation energy-   1004: Experimental value of solvation energy of a para-xylene    molecule-   1005: The number of atomic parameters-   1006: The number of atomic parameters of a para-xylene molecule-   1101: Atomic type-   1102: Atomic charge-   1103: Averaged bond distance-   1201: Atomic information-   1202: Atomic parameter value-   1203: Status of atomic parameter-   1204: Status of atomic parameter (value assigned)-   1205: Status of atomic parameter (value not assigned)-   1206: Molecular information-   1207: The number of “value assigned” atomic parameters contained in    a molecule-   1208: The number of “value not assigned” atomic parameters contained    in a molecule-   1209: Calculation status of the molecule-   1210: Initial value of molecular information-   1211: Initial value of number of “value assigned” atomic parameters    contained in the molecule-   1212: Initial value of Number of “value not assigned” atomic    parameters contained in the molecule-   1213: Initial value of calculation status of the molecular-   1301: Calculation order list-   1302: The input file generation step-   1303: Input file for solvation energy calculation-   1304: The salvation energy calculation job input step-   1305: Computer-   1306: Solvation energy calculation program-   1307: The calculation result outputting step-   1308: Output file for salvation energy calculation result-   1309: The output result processing step-   1401: Atomic parameter value-   1402: Value of an atomic attribute-   1403: Atom having “value assigned” atomic parameter-   1404: Atom having “value not assigned” atomic parameter-   1405: A linear function correlating atomic parameter value with    value of an atomic attribute-   1406: Value of an atomic attribute of a “value not assigned” atom-   1407: “Value not assigned” atom having value of an atomic attribute    far apart from value of an atomic attribute of a “value assigned”    atom-   1501: Atomic parameter value-   1502: Atomic charge-   1503: Averaged bond distance-   1504: Atom having “value assigned” atomic parameter-   1505: Atom having “value not assigned” atomic parameter-   1506: A linear function correlating atomic parameter value with    value of an atomic attribute-   1507: Atomic charge and averaged bond distance of a “value not    assigned” atom-   1508: “Value not assigned” atom having value of an atomic attribute    far apart from value of an atomic attribute of a “value assigned”    atom-   1601: Atomic type-   1602: Determination process of atomic parameter value-   1603: Atomic type that each atom contains-   1604: Molecule having the number of undetermined atomic parameter of    1-   1605: Atomic parameter r_(CH3)-   1606: Atomic parameter r_(CH3)-   1607: Undetermined atomic parameter-   1608: The number of undetermined atomic parameters-   1609: Molecule having the number of undetermined atomic parameters    of 1-   1610: Four atomic parameters determined with respect to atomic type    NH₂-   1611: Atomic parameter r_(NH2)-   1701: Amount of calculation-   1702: Calculation error-   1703: Plot of lozenge marks-   1704: Plot of rectangular marks-   1801: Molecule-   1802: Experimental value of solvation energy-   1803: Calculation error in the prior art-   1804: Calculation error in Embodiment of this invention-   1805: Averaged absolute error-   1901: Input apparatus-   19011: Input of energy convergence threshold τ-   19012: Input of necessary information and experimental value for    calculation of analysis object-   19013: Input of elemental type and element attribute value of each    element-   1902: The initialization step-   19021: The elemental parameter initialization step-   19022: The sorting up step of all analysis objects by the number of    undetermined elemental parameters-   1903: Calculation order list generation step-   19031: The analysis objects selection step-   19032: The calculation order determination step-   1904: The one-variable equation solving step-   19041: The undetermined elemental parameter determination step-   19042: Calculation order list update step-   19043: Calculation order list termination judging step-   1905: The elemental parameters update step-   19051: The elemental parameter expression formula update step-   19052: The sorting up step of undetermined analysis objects by the    number of undetermined elemental parameters-   19053: The sorting down step of analysis objects with the identical    number of undetermined elemental parameters by the number of    elemental parameters-   19054: The undetermined analysis objects update step-   1906: The elemental parameter calculation termination judging step-   1907: The calculation error computing step-   1908: Output apparatus-   19081: Output of determined elemental parameters-   2001: Calculation order list generation step-   2002: First round process to be executed in calculation order list    generation step-   20021: The number of undetermined elemental parameters-   20022: Analysis object having the number of undetermined elemental    parameters of 1-   20023: Calculation order list-   2003: The one-variable equation solving step-   2004: First round process to be executed in the one-variable    equation solving step-   2005: The elemental parameters update step-   2006: First round process to be executed in the atomic parameters    update step-   20061: Elemental type corresponding to determined elemental    parameter-   20062: Elemental parameter of an elemental type a-   20063: Element, wherein elemental attribute value is apart from that    of element used for the parameter determination by certain threshold    or more-   20064: The number of undetermined elemental parameters-   20065: The number of elemental parameters-   2007: Second round process to be executed in calculation order list    generation step-   20071: The Number of undetermined elemental parameters-   20072: Analysis object having the number of undetermined elemental    parameters of 1-   20073: Calculation order list-   2008: Second round process to be executed in the one-variable    equation solving step-   2009: Second round process to be executed in the atomic parameters    update step-   20091: Elemental type corresponding to determined elemental    parameter-   20092: Elemental parameter of elemental type a-   2010: “Value assigned” element-   2011: “Value not assigned” (undetermined) element-   2101: Input apparatus-   21011: Input of acceptable energy error ε-   21012: Input of energy convergence threshold τ-   21013: Input of three-dimensional coordinate information and    experimental value of salvation energy for molecule-   21014: Input of atomic type, atomic charge and averaged bond    distance for each atom-   2102: The initialization step-   21021: The atomic parameter initialization step-   21022: The sorting up step of all molecules by the number of    undetermined atomic parameters-   2103: The calculation order list generation step-   21031: The molecule selection step-   21032: The calculation order determination step-   2104: The one-variable equation solving step-   21041: The judgment step whether the molecule on the top of    calculation order list contains undetermined atomic parameters or    not-   21042: The undetermined atomic parameter determination step-   21043: The calculation error computing step-   21044: The step for comparing the calculation error with the    acceptable error-   21045: The setting afresh step of undetermined atomic parameter-   21046: Calculation order list update step-   21047: Calculation order list termination judging step-   2105: The atomic parameters update step-   21051: The atomic parameter expression formula update step-   21052: The step for tentatively determining some or all of    undetermined atomic parameters.-   21053: The sorting up step of undetermined molecules by the number    of undetermined atomic parameters-   21054: The sorting down step of molecules with the identical number    of undetermined atomic parameters by the number of atomic parameters-   21055: The undetermined molecule update step-   2106: The atomic parameter calculation termination judging step-   2107: Output apparatus-   21071: Output of value of determined atomic parameters-   2201: The calculation order list generation step-   2202: First round process to be executed in the calculation order    list generation step-   22021: The number of undetermined atomic parameters-   22022: Molecule having the number of undetermined atomic parameters    of 1 or less-   22023: Calculation order list-   2203: The one-variable equation solving step-   2204: First round process to be executed in the one-variable    equation solving step-   2205: The atomic parameters update step-   2206: First round process to be executed in the atomic parameters    update step-   22061: Atomic type corresponding to determined atomic parameter-   22062: Atomic parameter of atomic type a-   22063: Atom, wherein atomic charge is apart from that of other atom    belonging to the identical atomic type by certain threshold or more-   22064: The number of undetermined atomic parameters-   22065: The number of atomic parameters-   2207: Second round process to be executed in calculation order list    generation step-   22071: The number of undetermined atomic parameters-   22072: Molecule having the number of undetermined atomic parameters    of 1 or less-   22073: Calculation order list-   2208: Second round process to be executed in the one-variable    equation solving step-   2209: Second round process to be executed in the atomic parameters    update step-   22091: Atomic type corresponding to determined atomic parameter-   22092: Atomic parameter of atomic type a-   2210: “Value assigned” (determined) atom-   2211: “Value assigned” (tentatively determined) atom-   2212: “Value not assigned” (undetermined) atom-   2301: Start-   2302: The new setting judgment step of undetermined parameter-   2303: Delete process of all calculation order list-   2304: Delete process of molecule on the top from a calculation order    list-   2305: Calculation order list termination judging step-   2306: Termination (proceed to the atomic parameters update step).-   2307: Termination (proceed to the undetermined atomic parameter    determination step).-   2401: Atomic parameter value-   2402: One value of an atomic attribute-   2403: “Value assigned” atom-   2404: “Value not assigned” atom-   2405: A linear function correlating atomic parameter value with    value of an atomic attribute-   2406: Value of an atomic attribute of a “value not assigned” atom-   2407: Atom having value of tentatively determined atomic parameter    set as undetermined atomic parameter as it is-   2408: Atom having re-determined atomic parameter, after tentatively    determined atomic parameter value being set as undetermined atomic    parameter-   2409: Three regions based on value of an atomic attribute-   2410: A linear function defined in each region-   2501: Atomic parameter value.-   2502: Atomic charge.-   2503: Averaged bond distance.-   2504: “Value assigned” atom-   2505: “Value not assigned” atom-   2506: A linear function correlating atomic parameter value with    value of an atomic attribute-   2507: Atomic charge and averaged bond distance of a “value not    assigned” atom-   2508: Atom, which the tentatively determined value became the    determined value as it is-   2509: Atom, which the tentatively determined value was set as    undetermined atomic parameter, and atomic parameter was    re-determined-   2510: Two regions on a plane formed by atomic charge and averaged    bond distance-   2511: A linear function defined in each region-   2601: The early calculation stage-   2602: The last calculation stage-   2603: The amount of calculation for molecule n in the prior art-   2604: The amount of calculation for molecule n in this invention-   2605: The amount of calculation required for calculation of solvent    energy in one time-   2701: Averaged number of iteration-   2702: The amount of calculation in using Embodiment of this    invention-   2703: The lower bound of the amount of calculation using a    gradient-matrix-   2801: Input apparatus-   28011: Input of acceptable error ε-   28012: Input of convergence threshold τ-   28013: Input of necessary information and experimental value for    calculation of analysis object-   28014: Input of elemental type and value of element attribute for    each element-   2802: The initialization step-   28021: The elemental parameter initialization step-   28022: The sorting up step of all analysis objects by the number of    undetermined elemental parameters-   2803: Calculation order list generation step-   28031: The analysis objects selection step-   28032: The calculation order determination step-   2804: The one-variable equation solving step-   28041: The judgment step of whether an analysis object on the top of    a calculation order list contains undetermined elemental parameter    or not-   28042: The undetermined elemental parameter determination step-   28043: The calculation error computing step-   28044: The step for comparing the calculation error with the    acceptable error-   28045: The setting afresh step of undetermined elemental parameter-   28046: Calculation order list update step-   28047: Calculation order list termination judging step-   2805: The elemental parameters update step-   28051: The elemental parameter expression formula update step-   28052: The tentatively determining step of some or all of values of    elemental parameters of undetermined element-   28053: The sorting up step of undetermined analysis objects by    number of undetermined elemental parameters-   28054: The sorting down step of analysis objects with the identical    number of undetermined elemental parameters by number of elemental    parameters-   28055: The undetermined analysis object update step-   2806: The elemental parameter calculation termination judging step-   2807: Output apparatus-   28071: Output of determined elemental parameters-   2901: Calculation order list generation step-   2902: First round process to be executed in calculation order list    generation step-   29021: The number of undetermined elemental parameters-   29022: Analysis object having the number of undetermined elemental    parameters of 1 or less-   29023: Calculation order list-   2903: The one-variable equation solving step-   2904: First round process to be executed in the one-variable    equation solving step-   2905: The elemental parameters update step-   2906: First round process to be executed in the elemental parameters    update step-   29061: Elemental type corresponding to determined elemental    parameter-   29062: Elemental parameter of the elemental type a-   29063: Element, wherein elemental attribute value is apart from that    of other element belonging to the identical elemental type by    certain threshold or more-   29064: The number of undetermined elemental parameters-   29065: The number of elemental parameters-   2907: Second round process to be executed in calculation order list    generation step-   29071: The number of undetermined elemental parameters-   29072: Analysis object having the number of undetermined elemental    parameters of 1 or less-   29073: Calculation order list-   2908: Second round process to be executed in the one-variable    equation solving step-   2909: Second round process to be executed in the atomic parameters    update step-   29091: Elemental type corresponding to determined elemental    parameter-   29092: Elemental parameter of an elemental type a-   2910: “Value assigned” (determined) element-   2911: “Value assigned” (tentatively assigned) element-   2912: “Value not assigned” (undetermined) element-   3001: The input step-   3002: The initialization step-   3003: The calculation order list generation step-   30031: Inner process-   30032: The calculation order list display step-   30033: The calculation progress display step-   3004: The equation solving step-   3005: The atomic parameters update step-   30051: Inner process-   30052: The atomic parameter display step-   3006: The termination judging step-   3007: The output step-   3101: Display object displaying tab-   31011: Calculation order list tab-   31021: Calculation order list-   31022: Up-arrow button-   31023: Down-arrow button-   31024: Delete button-   31025: Confirm button-   3102: Calculation order display region-   3103: Distribution diagram display region-   3104: Molecular structure map display region-   3201: Display object displaying tab-   32011: Progress tab-   3202: Display region of summary of the atomic parameter calculation    progress-   3203: Display region of the atomic parameter calculation progress    for each molecule-   3301: Display object displaying tab-   33011: Atomic parameter tab-   3302: Display region of the atomic parameter determination status-   3303: Display region of atomic parameter value

It should be further understood by those skilled in the art thatalthough the foregoing description has been made on embodiments of theinvention, the invention is not limited thereto and various changes andmodifications may be made without departing from the spirit of theinvention and the scope of the appended claims.

1. A simulation parameter determination method, which is a method forelemental parameter determination necessary to reproduce, by simulationcalculation, experimental value of characteristic value or propertyvalue measured on analysis objects of any of a plurality kinds ofmolecules, materials, parts or structures, each analysis object beingcomposed of a plurality of one or a plurality of elements, each elementbeing classified into one of a plurality kinds of elemental type s, oreach element having one or a plurality of values of elementalattributes, wherein (1) in the input step, (1-1) acceptable error ε thatis maximum value acceptable to difference between calculated valueobtained by simulation, and experimental value; (1-2) convergencethreshold τ that is standard value to judge convergence of calculatedvalue; (1-3) information necessary for calculation of each analysisobject, and experimental value for each analysis object; and (1-4)elemental type for each element composing the analysis object, and valueof elemental attribute of each element composing the analysis object areinput into a memory unit, (2) in the pre-processing step, (2-1) value ofelemental parameter by each elemental type is initialized; and (2-2) adata set containing undetermined elemental parameter number on all ofthe analysis objects is present, and arrangement order of the data setis sorted up by the number of undetermined atomic parameters, (3) incalculation order list generation step, (3-1) an analysis object, havingthe number of undetermined elemental parameters of 1 or less, isselected from analysis objects containing undetermined elementalparameters; and (3-2) a calculation order list is generated based onre-arranged order at the above (2-2), of the selected analysis objects,as calculation order, (4) in the solving step of a one-variableequation, (4-1) only in the case where an analysis object on the top ofcalculation order list contains undetermined elemental parameter,solving of a one-variable equation for determination of undeterminedparameters is iterated until the amount of change of calculated valuebecomes below convergence threshold, to determine undetermined elementalparameter, and in the case where an analysis object on the top ofcalculation order list does not contain undetermined elementalparameter, process is forwarded to the following step (4-2); (4-2)calculation error, that is difference between calculated value of saidanalysis object using determined elemental parameter and experimentalvalue, is calculated; (4-3) absolute value of said calculation error,and said acceptable error are compared; (4-4) in the case where saidcalculation error is over the acceptable error, one of the tentativelydetermined elemental parameters is set newly as an undeterminedelemental parameter to return to the step (4-1), and in the case wheresaid calculation error is not over the acceptable error, process isforwarded to the following step (4-5); and (4-5) in the case where saidcalculation error is equal to or below the acceptable error, a data seton the top position of calculation order list is deleted; in the casewhere an analysis object is present on the top of calculation orderlist, process returns to the step (4-1); and in the case wherecalculation order list is empty, process is forwarded to the step (5),(5) in the elemental parameters update step, (5-1) elemental parameterof corresponding elemental type is updated, as a function of value ofelemental attribute, using an elemental parameter determined in theabove one-variable equation solving step; (5-2) some or all undeterminedelemental parameters, which is classified to said elemental type, aretentatively determined, using a function describing value of elementalparameter of the updated elemental type; (5-3) a plurality of data setsof analysis objects including undetermined elemental parameters aresorted up by the number of undetermined atomic parameters; (5-4)subsequent to the above (5-3), analysis objects with the same number ofundetermined atomic parameters are sorted down by the number ofelemental parameters; and (5-5) whether all of or at least some of eachof parameters of the data sets including undetermined elementalparameters is determined or not, and (6) whether undetermined analysisobjects are present or not, is judged, and in the case whereundetermined analysis objects are present, process returns to the abovestep (3), and in the case where undetermined analysis objects are notpresent, process terminates.
 2. A simulation parameter determinationmethod, which is a method for elemental parameter determinationnecessary to reproduce, by simulation calculation, experimental value ofcharacteristic value or property value measured on analysis objects ofany of a plurality kinds of molecules, materials, parts or structures,each analysis object being composed of a plurality of one or a pluralityof elements, each element being classified into one of a plurality kindsof elemental type s, or each element having one or a plurality of valuesof elemental attributes, wherein (1) in the input step, (1-1)convergence threshold τ that is standard value to judge convergence ofcalculated value; (1-2) three-dimensional coordinate information ofelements composing the analysis object, necessary for calculation ofexperimental value for each analysis object, or experimental value foreach analysis object; and (1-3) elemental type for each elementcomposing the analysis object, and value of elemental attribute of eachelement composing the analysis object are input into a memory unit, (2)in the pre-processing step, (2-1) value of elemental parameter by eachelemental type is initialized; and (2-2) a data set containingundetermined elemental parameter number on all of the analysis objectsis present, and arrangement order of the data set is sorted up by thenumber of undetermined atomic parameters, (3) in calculation order listgeneration step, (3-1) an analysis object, having the number ofundetermined elemental parameters of 1, is selected from analysisobjects containing undetermined elemental parameters; and (3-2) acalculation order list is generated based on re-arranged order at theabove (2-2), of the selected analysis objects, as calculation order, (4)in the solving step of a one-variable equation, (4-1) on an analysisobject on the top of calculation order list, solving of a one-variableequation for determination of undetermined parameters is iterated untilthe amount of change of calculated value becomes below convergencethreshold, to determine undetermined elemental parameter; and (4-2) adata set on the top position of calculation order list is deleted; andin the case where an analysis object is present on the top ofcalculation order list, process returns to the step (4-1); and in thecase where calculation order list is empty, process is forwarded to thestep (5), (5) in the elemental parameters update step, (5-1) elementalparameter of corresponding elemental type is updated, as a function ofvalue of elemental attribute, using an elemental parameter determined inthe above one-variable equation solving step; (5-2) a plurality of datasets of analysis objects including undetermined elemental parameters aresorted up by the number of undetermined elemental parameters; (5-3)subsequent to the above (5-2), analysis objects with the same number ofundetermined elemental parameters are sorted down by the number ofelemental parameters; and (5-4) whether all of or al least some of eachof parameters of the data sets of analysis objects includingundetermined elemental parameters is determined or not, and (6) whetherundetermined analysis objects are present or not, is judged, and in thecase where undetermined analysis objects are present, process returns tothe above step (3), and in the case where undetermined analysis objectsare not present, process terminates.
 3. A simulation parameterdetermination method, which is a method for atomic parameterdetermination necessary to reproduce, by simulation calculation,experimental value of each solvation energy measured on a pluralitykinds of molecules, each molecule being composed of a plurality ofatoms, each atom being classified into one of a plurality kinds ofatomic types, or each atom having one or a plurality of values of atomicattributes, wherein (1) in the input step, (1-1) acceptable energy errore that is maximum value acceptable to difference between calculatedvalue of salvation energy obtained by simulation calculation, andexperimental value of solvation energy; (1-2) energy convergencethreshold τ that is standard value to judge convergence of calculatedvalue of solvation energy; (1-3) three-dimensional coordinateinformation of atoms composing the molecule, necessary for calculationof experimental value salvation energy for each molecule, orexperimental value of solvation energy for each molecule; and (1-4)atomic type for each atom composing the molecule, and value of an atomicattribute of each atom composing the molecule are input into a memoryunit, (2) in the pre-processing step, (2-1) atomic parameter value byeach atomic type is initialized; and (2-2) a data set containingundetermined atomic parameter number on all of the molecules is present,and arrangement order of the data set is sorted up by the number ofundetermined atomic parameters, (3) in calculation order list generationstep, (3-1) a molecule, having the number of undetermined atomicparameters of 1 or less, is selected from molecules containingundetermined atomic parameters; and (3-2) a calculation order list isgenerated based on re-arranged order at the above (2-2), of the selectedmolecules, as calculation order, (4) in the solving step of aone-variable equation, (4-1) only in the case where an molecule on thetop of calculation order list contains undetermined atomic parameter,solving of a one-variable equation for determination of undeterminedparameters is iterated until the amount of change of calculated value ofsolvation energy becomes below energy convergence threshold, todetermine undetermined parameter, and in the case where a molecule onthe top of calculation order list does not contain undetermined atomicparameter, process is forwarded to the following step (4-2); (4-2)calculation error, that is difference between calculated value of saidmolecule using determined atomic parameter and experimental value, iscalculated; (4-3) absolute value of said calculation error, and saidacceptable energy error are compared; (4-4) in the case where saidenergy calculation error is over the acceptable energy error, one of thetentatively determined atomic parameters is set newly as an undeterminedatomic parameter to return to the step (4-1), and in the case where saidenergy calculation error is not over the acceptable energy error,process is forwarded to the following step (4-5); and (4-5) in the casewhere said calculation error is equal to or below the acceptable error,a data set on the top position of calculation order list is deleted; inthe case where a molecule is present on the top of calculation orderlist, process returns to the step (4-1); and in the case wherecalculation order list is empty, process is forwarded to the step (5),(5) in the atomic parameters update step, (5-1) atomic parameter ofcorresponding atomic type is updated, as a function of value of anatomic attribute, using an atomic parameter determined in the aboveone-variable equation solving step; (5-2) some or all of undeterminedatomic parameters, which is classified to said atomic type, aretentatively determined, using a function describing atomic parametervalue of the updated atomic type; (5-3) a plurality of data sets ofmolecules including undetermined atomic parameters are sorted up by thenumber of undetermined atomic parameters; (5-4) subsequent to the above(5-3), molecules with the same number of undetermined atomic parametersare sorted down by the number of atomic parameters; and (5-5) whetherall of or al least some of each of parameters of the data sets ofmolecules including undetermined atomic parameters is determined or not,and (6) whether undetermined molecules are present or not, is judged,and in the case where undetermined molecules are present, processreturns to the above step (3), and in the case where undeterminedmolecules are not present, process terminates.
 4. A simulation parameterdetermination method, which is a method for atomic parameterdetermination necessary to reproduce, by simulation calculation,experimental value of each solvation energy measured on a pluralitykinds of molecules, each molecule being composed of a plurality ofatoms, each atom being classified into one of a plurality kinds ofatomic types, or each atom having one or a plurality of values of atomicattributes, wherein (1) in the input step, (1-1) energy convergencethreshold τ that is standard value to judge convergence of calculatedvalue of solvation energy; (1-2) three-dimensional coordinateinformation of atoms composing the molecule, necessary for calculationof experimental value salvation energy for each molecule, orexperimental value of solvation energy for each molecule; and (1-3)atomic type for each atom composing the molecule, and value of an atomicattribute of each atom composing the molecule are input into a memoryunit, (2) in the pre-processing step, (2-1) atomic parameter value byeach atomic type is initialized; and (2-2) a data set containingundetermined atomic parameter number on all of the molecules is present,and arrangement order of the data set is sorted up by the number ofundetermined atomic parameters, (3) in calculation order list generationstep, (3-1) a molecule, having the number of undetermined atomicparameters of 1, is selected from molecules containing undeterminedatomic parameters; and (3-2) a calculation order list is generated basedon re-arranged order at the above (2-2), of the selected molecules, ascalculation order, (4) in the solving step of a one-variable equation,(4-1) solving of a one-variable equation for determination ofundetermined parameters is iterated until the amount of change ofcalculated value of salvation energy becomes below convergencethreshold, to determine undetermined parameter, on a molecule on the topof calculation order list; and (4-2) a data set on the top position ofcalculation order list is deleted; in the case where a molecule ispresent on the top of calculation order list, process returns to thestep (4-1); and in the case where calculation order list is empty,process is forwarded to the step (5), (5) in the atomic parametersupdate step, (5-1) atomic parameter of corresponding atomic type isupdated, as a function of value of an atomic attribute, using an atomicparameter determined in the above one-variable equation solving step;(5-2) a plurality of data sets of molecules including undeterminedatomic parameters are sorted up by the number of undetermined atomicparameters; (5-3) subsequent to the above (5-2), molecules with the samenumber of undetermined atomic parameters are sorted down by the numberof atomic parameters; and (5-4) whether all of or al least some of eachof parameters of the data sets of molecules including undeterminedatomic parameters is determined or not, and (6) whether undeterminedmolecules are present or not, is judged, and in the case whereundetermined molecules are present, process returns to the above step(3), and in the case where undetermined molecules are not present,process terminates.
 5. The simulation parameter determination methodaccording to claim 3, wherein user interface is provided with functionthat, in said calculation order list generation step, when calculationorder is displayed, and one molecule in said calculation order isselected, an atomic distribution map at a plane formed by atomic chargeand averaged bond distance, and a molecular structure map that expressesthe atomic parameter determination status of said selected molecule, bya three-dimensional structure of the molecular, and spheres drawn oneach atom composing the molecule, in an overlapped way, are displayed,as for an atomic type to which undetermined atomic parameter of saidselected molecule is classified, and a user can change calculation orderbased on these sets of display information.
 6. The simulation parameterdetermination method according to claim 4, wherein user interface isprovided with function that, in said calculation order list generationstep, when calculation order is displayed, and one molecule in saidcalculation order is selected, an atomic distribution map at a planeformed by atomic charge and averaged bond distance, and a molecularstructure map that expresses the atomic parameter determination statusof said selected molecule, by a three-dimensional structure of themolecular, and spheres drawn on each atom composing the molecule, in anoverlapped way, are displayed, as for an atomic type to whichundetermined atomic parameter of said selected molecule is classified,and a user can change calculation order based on these sets of displayinformation.
 7. The simulation parameter determination method accordingto claim 3, wherein user interface is provided with function that, insaid calculation order list generation step, after generation ofcalculation order list, or after a user executes re-arrangement ordeletion of molecules in calculation order list, summary result of acalculation status of the molecule, such as “value assigned”, “inprogress”, or “undetermined”, and calculation elapsed time aredisplayed, as summary of a progress of atomic parameter calculation, ora calculation status, the number of atomic parameters and the number ofundetermined atomic parameters of each atom are displayed, as summary ofa progress of atomic parameter of each atom.
 8. The simulation parameterdetermination method according to claim 4, wherein user interface isprovided with function that, in said calculation order list generationstep, after generation of calculation order list, or after a userexecutes re-arrangement or deletion of molecules in calculation orderlist, summary result of a calculation status of the molecule, such as“value assigned”, “in progress”, or “undetermined”, and calculationelapsed time are displayed, as summary of a progress of atomic parametercalculation, or a calculation status, the number of atomic parametersand the number of undetermined atomic parameters of each atom aredisplayed, as summary of a progress of atomic parameter of each atom. 9.The simulation parameter determination method according to claim 3,wherein user interface is provided with function that, in said atomicparameters update step, the number of all atoms, the number of atomshaving determined atomic parameter, the number of tentatively determinedatoms and the number of undetermined atoms are displayed by each atomictype, as the atomic parameter determination status of each atomic type,and when one atomic type is selected, an atomic parameter of an atombelonging to said atomic type is displayed in space formed by atomiccharge, averaged bond distance and atomic parameter.
 10. The simulationparameter determination method according to claim 4, wherein userinterface is provided with function that, in said atomic parametersupdate step, the number of all atoms, the number of atoms havingdetermined atomic parameter, the number of tentatively determined atomsand the number of undetermined atoms are displayed by each atomic type,as the atomic parameter determination status of each atomic type, andwhen one atomic type is selected, an atomic parameter of an atombelonging to said atomic type is displayed in space formed by atomiccharge, averaged bond distance and atomic parameter.